Systems and methods for configuring a communications network

ABSTRACT

Systems and methods are disclosed for configuring a communications network. In disclosed embodiments, a set of permissible service link decompositions and a set of basic service links may be obtained for the communications network. A spanning subset of service links for the communications may be generated. Generation of the spanning subset may include selecting a decomposition of a first service link from a set of permissible service link decompositions; updating the set of permissible service link decompositions based on the selected decomposition; and updating the set of basic service links using the updated set of permissible service link decompositions. In some embodiments, obtaining the set of permissible service link decompositions can include generating a set of permissible service link decompositions by traversing decomposition graphs generated for each of the service links. In some embodiments, the communications network can be configured to satisfy network demands using the spanning subset.

BACKGROUND

Communications networks, such as optical communications networks, can berepresented by nodes, each corresponding to one or more signal handlingdevices, connected by edges, corresponding to one or more signalpathways. Service links can be created to satisfy demands on thecommunications network. Such service links may have differenttransceiver data types (e.g., depending on the signal handling device(s)used to implement the service link). Multiple sets of service links maybe able to satisfy the demands on the network. The service links inthese differing sets may differ in terms of number, transceiver datatype, or pathway. Therefore, selection of a set of service links tosatisfy the demands on a network may implicate considerations ofutilization, quality, lifespan or maintenance, cost, or the like.

SUMMARY

The disclosed systems and methods can be used to configure acommunications network. The communications network can be configured toimplement service links that satisfy demands on the communicationsnetwork. Disclosed embodiments can be used to determine low-weight setsof service links (where weights can represent utilization, quality,lifespan or maintenance, cost, or other such considerations) or spanningsets of service links capable of satisfying the demands on the network.

The disclosed embodiments include a method for determining a spanningsubset of service links for a communications network. The method caninclude obtaining a set of permissible service link decompositions forthe communications network and a set of basic service links for thecommunications network. The method can further include generating thespanning subset. Generating the spanning subset can including selectinga decomposition of a first service link from the set of permissibleservice link decompositions. Generating the spanning subset can furtherinclude updating the set of permissible service link decompositionsbased on the selected decomposition. Generating the spanning subset canalso include updating the set of basic service links using the updatedset of permissible service link decompositions.

The disclosed embodiments include a method for configuring acommunications network. The method can include obtaining a set ofpermissible decompositions of a set of service links for thecommunications network. The method can further include iterativelydetermining a spanning subset of the set of service links. An iterationof the determination of the spanning subset can include updating thespanning subset of the set of service links based on the set ofpermissible service link decompositions. An iteration can furtherinclude updating the set of permissible service link decompositionsbased on the spanning subset. An iteration can also include selecting,from the set of permissible service link decompositions, a decompositionof a first service link. An iteration can further include updating theset of permissible service link decompositions using a first demandassociated with the first service link. The method can also includeconfiguring the communications network to transmit network traffic usingthe spanning subset of service links.

The disclosed embodiments include an additional method for configuring acommunication network. The additional method includes determining a setof service links for a path in the communication network based on a setof demands for the path. The determination can include repeatedlyselecting sets of service links for segments of the path. A repeat for asegment can include determining pair weights for path pairs. Each pathpair can include an initial portion of the segment, the initial portionbeing associated with a first set of service links and a first weightdependent on the first set. Each path pair can also include acomplementary portion of the segment, the complementary portion beingassociated with a second set of service links and a second weightdependent on the second set. The pair weight for the each path pair candepend on the first weight and the second weight. A repeat for a segmentcan further include selecting a path pair for the segment based on thepair weight for the selected path pair. A repeat for a segment can alsoinclude selecting the first and second sets of service links for theselected path pair as the set of service links for the segment. Thedetermination of the set of service links can further includedetermining, when the segment comprises the path, the set of servicelinks for the segment as the set of service links for the path. Themethod can further include configuring the communication network toservice the set of demands for the path using the selected set ofservice links for the path.

The disclosed embodiments include a method for determining aconfiguration of a communication network. The method can includeobtaining, for a communication network comprising fiber optic cablesconnected by switches and transceiver-transponders, a representation ofthe communication network as a set of edges representing the fiber opticcables, the edges connected by nodes representing the switches andtransceiver-transponders. The method can further include determining aset of service links for a path in the communication network based on aset of demands for the path, each service link representing datatransmission by one of the transceiver-transponders through one or moreof the fiber optic cables connected by zero or more of the switches. Thedetermination of the set of service links can include iterativelyselecting sets of service links for progressively longer initialsegments of the path. An iteration for an initial segment can includedetermining pair weights for path pairs. Each path pair can include aninitial portion of the initial segment, the initial portion beingassociated with a first set of service links and a first weightdependent on the first set. Each path pair can also include acomplementary portion of the initial segment, the complementary portionbeing associated with a second set of service links and a second weightdependent on the second set. The pair weight for the each path pair candepend on the first weight and the second weight. An iteration for aninitial segment can further include selecting a path pair for theinitial segment based on the pair weight for the selected path pair. Aniteration for an initial segment can also include selecting the firstand second sets of service links for the selected path pair as the setof service links for the initial segment. The determination of a set ofservice links can further include determining, when the initial segmentcomprises the path, the set of service links for the initial segment asthe set of service links for the path.

The disclosed embodiments include a method for determining a spanningset of service links for a communications network. The method caninclude obtaining a set of service links for a cycle graph representinga communications network. The set of service links can include a firstsubset of first service links, each of the first service linkstraversing at most a first number of edges in the cycle graph andassociated with one of first demands having a first demand capacity. Theset of service links can include a second subset of second servicelinks, each of the second service links traversing at most a secondnumber of edges in the cycle graph and associated with one of seconddemands having a second demand capacity. The set of service links caninclude a third subset of third service links, each of the third servicelinks traversing at least a third number of edges in the cycle graph andassociated with one of third demands having a third demand capacity. Afirst capacity bound of the first service links can be greater than orequal to the sum of the first demand capacity and two times the seconddemand capacity. The first capacity bound of the first service links canbe greater than or equal to the sum of the first demand capacity and thethird demand capacity. The first capacity bound of the first servicelinks can be less than the sum of the first demand capacity, the seconddemand capacity and the third demand capacity. The method furthercomprises determining a spanning subset of the service links containingthe first and second service links. The method also comprisesconfiguring the communications network to satisfy the first, second, andthird demands using the spanning subset of the service links.

The disclosed embodiments include an additional method for determining aspanning set of service links for a communications network. The methodcan include obtaining a graph including a first number of edges, thegraph representing the communications network. The method can furtherinclude obtaining transceiver data types. The transceiver data types caninclude a first transceiver data type with a first weight. A servicelink configured to use the first transceiver data type can be capable ofspanning one edge of the graph and satisfying a set of demands on thecommunications network. The transceiver data types can include a secondtransceiver data type with a second weight. A service link configured touse the second transceiver data type can be capable of spanning twoedges of the graph and satisfying at most some of the demands in the setof demands. The transceiver data types can include a third transceiverdata type with a third weight. A service link configured to use thethird transceiver data type can be capable of spanning three edges ofthe graph and satisfying one of the demands in the set of demands. Themethod can also include selecting, based on the first weight, secondweight, third weight, and first number of edges, service links thatsatisfy the demands. The selected service links can include a firstnumber of service links having the second transceiver data type, thefirst number of service links equal to the first number of edges; aservice link having the first transceiver data type and a second numberof service links having the second transceiver data type, the secondnumber of service links equal to the first number of edges minus one;four service links having the third transceiver data type and a thirdnumber of service links having the second transceiver data type, thethird number of service links equal to the first number of edges minusthree; a fourth number of service links having the third transceiverdata type, the fourth number of service links equal to four thirds timesthe first number of edges; a service link having the first transceiverdata type and a fifth number of service links having the thirdtransceiver data type, the fifth number of service links equal to fourthirds times the first number of edges minus one; or two service linkshaving the second transceiver data type and a sixth number of servicelinks having the third transceiver data type, the sixth number ofservice links equal to four thirds times the first number of edges minustwo. The method can further include configuring the communicationsnetwork to satisfy the set of demands using the determined servicelinks.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the disclosed embodiments, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings are not necessarily to scale or exhaustive. Instead,emphasis is generally placed upon illustrating the principles of theembodiments described herein. The accompanying drawings, which areincorporated in and constitute a part of this specification, illustrateseveral embodiments consistent with the disclosure and, together withthe description, serve to explain the principles of the disclosure. Inthe drawings:

FIG. 1 depicts an exemplary schematic of an exemplary communicationnetwork including a set of service links, consistent with disclosedembodiments.

FIG. 2 depicts an exemplary method for selecting a set of service linksthat satisfy a set of demands over a path along a communication network,consistent with disclosed embodiments.

FIG. 3 depicts an exemplary selection of service links for a path,consistent with disclosed embodiments.

FIG. 4 depicts an exemplary determination of a spanning subset ofservice links for an exemplary communication network, consistent withdisclosed embodiments.

FIG. 5 depicts an exemplary method for generating a spanning subset ofservice links for a communication network, consistent with disclosedembodiments.

FIG. 6 depicts an exemplary method for generating decompositions of aservice link, consistent with disclosed embodiments.

FIG. 7 depicts an exemplary decomposition graph for suitable fordetermining decompositions of a service link, consistent with disclosedembodiments.

FIG. 8 depicts an exemplary method of updating a set of permissibledecompositions, consistent with disclosed embodiments.

FIGS. 9A and 9B depict an exemplary determination of a spanning subsetof service links for a communications network represented by anexemplary cycle graph, consistent with disclosed embodiments.

DETAILED DESCRIPTION

Reference will now be made in detail to exemplary embodiments, discussedwith regards to the accompanying drawings. In some instances, the samereference numbers will be used throughout the drawings and the followingdescription to refer to the same or like parts. Unless otherwisedefined, technical and/or scientific terms have the meaning commonlyunderstood by one of ordinary skill in the art. The disclosedembodiments are described in sufficient detail to enable those skilledin the art to practice the disclosed embodiments. It is to be understoodthat other embodiments may be utilized and that changes may be madewithout departing from the scope of the disclosed embodiments. Forexample, unless otherwise indicated, method steps disclosed in thefigures can be rearranged, combined, or divided without departing fromthe envisioned embodiments. Similarly, additional steps may be added orsteps may be removed without departing from the envisioned embodiments.Thus, the materials, methods, and examples are illustrative only and arenot intended to be necessarily limiting.

Communications networks can be implemented using signal handling devicesto transmit data along signal pathways. The communications networks canbe associated with sets of demands and can be configurable to satisfythese sets of demands. A communications network may be configurable tosatisfy a set of demands in multiple different ways. Differentconfigurations may use different signal handling devices or signalpathways. Selection of a network configuration may therefore implicateconsiderations of utilization, quality, lifespan or maintenance, cost,or the like. Determination of an appropriate configuration may bedifficult, because of the large number of signal handling devices,demands, and signal pathways in the communications network.

The disclosed embodiments can enable the determination of networkconfigurations with favorable characteristics. Certain disclosedembodiments can enable selection of lower-weight sets of service linksthat satisfy demands over a path on a communications network. In suchembodiments, the weights can represent characteristics of interest, suchas utilization, quality, lifespan or maintenance, cost, or the like.Accordingly, such embodiments can improve the quality, efficiency, orother characteristics of a communications network. Additionally oralternatively, given a set of service links and an associated set ofdemands, certain disclosed embodiments can enable determination of asubset of the service links capable of satisfying the demands.Accordingly, such embodiments can reduce the number of service linksnecessary to satisfy the demands, improving the efficiency andflexibility of the communications network.

Path Generation

FIG. 1 depicts a schematic of an exemplary communication network 100including a set of service links, consistent with disclosed embodiments.Communication network 100 can be an optical communication network (e.g.,a fiber optic network), an electrical communication network (e.g., anethernet or PSTN network), or a hybrid network including optical andelectrical components. A schematic representation of communicationnetwork 100 can include nodes (e.g., N₁ to N₅) and edges (e.g., e₁ toe₄). Each node can represent one or more signal-handling devices, suchas switches (e.g., ethernet or optical switches), routers, transceivers,transponders, or the like. Each node may or may not includegeographically co-located signal-handling devices. Each edge canrepresent one or more signal pathways (e.g., a fiber optic cable foroptical signals, metal cable for electrical signals, or the like)connecting or potentially connecting two nodes. An edge can representmultiple signal pathways. For example, an edge can represent a multimodeoptical fiber, a single-mode optical fiber, and a copper cable, allconnecting or potentially connecting two nodes. In this example, thesingle-mode fiber and multi-mode fibers may originate and terminate atthe same or different optical transceivers/transponders or switches,while the copper cable may originate or terminate in an electricaltransceiver/transponder or switch (e.g., a telephone repeater, exchange,or the like). Accordingly, the schematic representation of thecommunications network can be a graph, with the nodes as verticesconnected by the edges. In some embodiments, the graph can be a cyclegraph (e.g., some number of vertices connected in a closed chain).

Consistent with disclosed embodiments, the elements of communicationnetwork 100 can be associated with network parameters. In someembodiments, an edge connecting two vertices can be associated with atleast one value of at least one metric. This metric value can be ordepend upon a characteristic of a signal pathway connecting orpotentially connecting the two nodes. In some embodiments, the metricvalue can be or depend upon a physical length of the signal pathwayconnecting or potentially connecting the two nodes. For example, whenthe signal pathway is an optical fiber, the length can be a physicallength (e.g., kilometers, miles, or the like) of the optical fiber, or ascaled physical length reflecting the quality or other transmissioncharacteristics of the optical fiber. Other possible metrics includesignal-to-noise ratio (e.g., an optical signal-to-noise ratio (ONSR) orthe like), attenuation, or similar signal pathways characteristics. Thedisclosed embodiments are not limited to any particular measure of themetric value and the descriptions provided herein use unitless numbersfor convenience of explanation. Furthermore, for convenience ofexplanation, the description provided herein refers to length as theexemplary metric. However, the disclosed embodiments should beunderstood to be generally applicable to any such metric. In variousembodiments, the communications network can be associated with one ormore transceiver data types. For example, one or more nodes of thecommunications network can be associated with a transceiver data type.In some instances, a transceiver data type can be associated with atransceiver-transponder or switch at a node. The transceiver data typecan describe aspects of the signal-handling capabilities of thetransceiver-transponder or switch. In some instances, a transceiver datatype for a transceiver-transponder can indicate a capacity bound oftransceiver-transponder or switch (e.g., a bound on bit rate, baud,bandwidth, or the like). The disclosed embodiments are not limited toany particular measure of capacity bound and the descriptions providedherein use unitless numbers for convenience of explanation. In variousinstances, a transceiver data type for a transceiver-transponder orswitch can indicate a length bound for signal transmission using thetransceiver-transponder or switch. The length bound can be a physicallength or a scaled physical length accounting for characteristics of thetransmission medium. The length bound can be a maximum length bound. Insome instances, a transceiver data type can be associated with a weight.A weight can be based on at least one of utilization considerations(e.g., indicating a preference for less-used transceiver-transponders),quality considerations (e.g., indicating a preference fortransceiver-transponders that provide a better signal quality), lifespanor maintenance considerations (e.g., indicating a preference fortransceiver-transponders with a greater remaining lifespan or requiringless frequent maintenance), cost considerations (e.g., a cost associatedwith usage of a transceiver-transponder), or other such considerations.

Consistent with disclosed embodiments, a service link l can be a tupleincluding an edge and a transceiver data type:l=(P,TD)

In this example, P is a path on the network including one or more edgesand TD is a transceiver data type. In some embodiments, the length ofthe path P can be the sum of the lengths associated with the edges. Invarious embodiments, the length of the path P must be less than thelength bound of the transceiver data TD.

FIG. 1 provides examples of potential service links on network 100,consistent with disclosed embodiments. As shown, network 100 can includepath 110 from node N₁ through node N₅ along edges e₁ to e₄. Eachsub-path along path 110 can be associated with one or more potentialservice links. For example, the sub-path from N₂ to N₃ is associatedwith potential service links S₄ and S₅. The nodes of network 100 caneach support at least one of two transceiver data types. In thisnon-limiting example, the first transceiver data TD₁ has a capacitybound of 200, a length bound of 800, and a weight of 17, while thesecond transceiver data TD₂ has a capacity bound of 100, a length boundof 1500, and a weight of 13. The two types of transceiver data canrepresent two different ways of conveying signals between nodes alongpath 110. For example, the first transceiver data type may correspond tousing one type of optical modulation (e.g. PSK, or the like), while thesecond transceiver data type may correspond to using another, more-denseoptical modulation (e.g. 256-QAM, or the like). To continue thisexample, more data can be provided a short distance using the densemodulation, while less data can be provided a longer distance withlesser BW using the less dense modulation (PSK).

In the non-limiting example depicted in FIG. 1, potential service linksindicated with solid lines may use TD₁ (e.g., S₂-S₆, S₉, S₁₀), whilepotential service links indicated with dotted lines may use TD₂ (e.g.,S₁, S₇, S₈, S₁₁, S₁₂). The potential service links associated with path110 of communication network 100 may depend on the lengths associatedwith the edges (e.g., edge e₁ can be associated with a length of 800 andedge e₄ can be associated with a length of 300, as shown). For example,a service link S₁₂ can begin at node N₂ and end at node N₅ because thetotal length of this path (e.g., 1400—the sum of the lengths of edges e₂to e₄) is less than the length bound for transceiver data TD₂ (e.g.,1500). A service link using transceiver data TD₁ and beginning at nodeN₂ and ending at node N₅ may not be possible, as the length bound fortransceiver data TD₁ is only 800.

A set of demands can be associated with path 110 over network 100. Suchdemands can arise from user requests for streaming video,videoconferencing applications, web surfing, or the like. The disclosedembodiments are not limited to any particular demand type or demandorigin. The set of demands can have an associated capacity (e.g., a bitrate, baud, bandwidth requirement, or the like). In some embodiments,the demand capacity can be a bound on the amount of resources that maybe requested or used to service the demand. The disclosed embodimentsare not limited to a particular measure of demand capacity and thedescriptions provided herein use unitless numbers for convenience ofexplanation. In some embodiments, the demand capacity may depend on thetype of demand (e.g., videoconferencing versus web surfing), aquality-of-service requirement associated with the demand, or the like.The disclosed embodiments are not limited to any particular type ororigin of the demand capacity.

A set of services links SL can satisfy a set of demands D havingcapacities X on the path P when there exists an association between eachdemand d∈D and a list of service links L(d), such that:L(d)={l ₁ ^(d) , . . . ,l _(k(d)) ^(d) },l _(i) ^(d) ∈SL

In some embodiments, concatenating the paths of the service links inL(d) results in the path P. In various embodiments, the sum of alldemand capacities for all demands using each service link (e.g., alldemands that include the service link in their associated lists ofservice links) is less than the capacity of that service link. Forexample:cap(r)≥Σ_(d:r∈L(d)) x _(d) ,∀l∈SL,∀d∈

In this equation, the sum of all demand capacities x for each demand dincluding the service link l in its list of service links L(d) can beless than the capacity associated with the service link l.

Two exemplary sets of service links, SLS₁ and SLS₂, are depicted inFIG. 1. SLS₁ includes the service links S₃, S₄, and S₂. Theconcatenation of these service links is path 110. Each of these linkshas capacity 200, while the total sum of the demand capacities for eachof these links is 160 (e.g., the sum of D₁, D₂, and D₃). SLS₂ includesthe service links S₁, S₂, S₁, and S₁₂. The concatenation of thecontiguous service links in SLS₂ (e.g., the concatenation of contiguousservice links S₁ and S₂, and the concatenation of the contiguous servicelinks S₁₁ and S₁₂) is also path 110. When demands D₁ and D₂ areassociated with service links S₁ and S₂, demand D₃ can be associatedwith service links S₁₁ and S₁₂. When demands D₁ and D₂ are associatedwith service links S₁₁ and S₁₂, demand D₃ can be associated with servicelinks S₁ and S₂. In either case, for each of service links S₁, S₂, S₁,and S₁₂, the total sum of demand capacities associated with the servicelink is less than the capacity of the service link.

While the sets of service links SLS₁ and SLS₂ both satisfy the demandsd₁, d₂, and d₃, different total weights are associated with these twosets of service links. The total weight associated with SLS₁ is 51,while the total weight associated with SLS₂ is 59. Accordingly, SLS₂ hasa higher weight than SLS₁. As the weights may represent utilization,quality, lifespan or maintenance, cost, or other considerations (or somecombination thereof), communications network 100 may be configured tosatisfy demands d₁, d₂, and d₃ by routing communications associated withthese demands through the service links in SLS₁. For example, acontroller of communications network 100 can configure one or moreswitches or transceiver-transponders at node n₁ to route trafficassociated with demands d₁, d₂, and d₃ through service link S₃. Thecontroller can configure one or more transceiver-transponders at node N₂to route traffic associated with demands d₁, d₂, and d₃ through servicelink S₄. Finally, the controller can configure one or more switches ortransceiver-transponders at node N₃ to route traffic associated withdemands d₁, d₂, and d₃ through service link S₂. In this manner, thecontroller can configure the network to satisfy the demands d₁, d₂, andd₃ using a set of service links having lesser total weight.

FIG. 2 depicts a method 200 for selecting a set of service links thatsatisfy a set of demands over a path along a communication network,consistent with disclosed embodiments. In some embodiments,communication network 100 can include fiber optic cables connected byswitches and transceiver-transponders. In various embodiments, a servicelink can represent data transmission by one of thetransceiver-transponders through one or more of the fiber optic cablesconnected by zero or more of the switches. Method 200 is not limited tooptical networks, but can also be used for electronic and hybridoptical/electronic networks.

Method 200 can enable selection of a set of service links with lesserweights, without requiring a comprehensive evaluation of every potentialarrangement of service links. While the explanatory example in FIG. 1included five nodes and two sets of transmission data, a real-worldexample might include between 3 and 600 nodes (or more) and 2 to 20different sets of transmission data (or more). In such a scenario, theremay be twelve thousand (or more) potential service links. Accordingly,determining the set of service links having the minimal total weight mayrequire an infeasible amount of time or computing resources.

Consistent with disclosed embodiments, method 200 can includedetermining a set of service links for the path. The computing devicecan determine the set of service links for the path by repeatedly oriteratively determining sets of service links for segments of the path.Determining the set of service links for a segment can include dividingthe segment into a path pair including an initial sub-segment and acomplementary sub-segment. The computing device can be configured todetermine a division of the segment and to determine sets of servicelinks for the initial sub-segment and a complementary sub-segment thatminimize the total weight associated with the segment. In the nextrepeat or iteration, the segment can be extended to include anadditional portion of the path. The computing device can then repeat thedetermination of a path pair having sets of service links that minimizethe total weight associated with the segment.

In some embodiments, given a path P including edges {e₀, . . . ,e_(n-1)} and subject to demands D, the computing device can determineweights w(p_(i,j), D) for sub-paths p_(i,j)=(e_(i), . . . , e_(j)). Thenthe computing device can iteratively determine:

${\overset{¯}{w}\left( {p_{0,j},D} \right)} = {\min\limits_{i \in {\{{1,\ldots,{j - 1}}\rbrack}}\left( {{\overset{\_}{w}\left( {p_{0,i},D} \right)} + {w\left( {p_{{i + 1},j},D} \right)}} \right)}$for  j = 1, …  , n − 1

Determining sets of service links for the sub-paths may be morecomputationally tractable than determining a set of service links forthe overall path. The set of service links for the path can be the unionof the sets of service links for the sub-paths. The total weight for theoptimal set of service links for the overall path may then bounded aboveby the sum of the total weights for each sub-path. Accordingly, whetherthe weights reflect utilization, quality, lifespan or maintenance, cost,or other considerations (or some combination thereof), method 200 can beused to configure the network to better address these considerations.Thus, method 200 can be used to improve the operation of communicationsnetwork 100.

In some embodiments, the computing device can perform method 200repeatedly or periodically. For example, the computing device canperform method 200 upon expiration of an interval between 30 seconds and5 minutes, or longer. In various embodiments, the computing device canperform method 200 in response to obtaining a request or new demand, anew type of transmission data, a new node, a change in weights, or thelike. In some embodiments, the computing device can perform method 200in response to a warning or error condition, such as exceeding thecapacity of a service link, a decrease in a quality of service, or asimilar condition.

In step 210 of method 200, a computing device associated with acommunication network (e.g., communication network 100) can obtain apath, a set of demands, and one or more transceiver data types. In someembodiments, the computing device can receive a representation of thecommunication device as a set of edges representing fiber optic cables,the edges being connected by nodes representing the switches andtransceiver-transponders. The path can be from an origin node in therepresentation of the communication network to a destination node in therepresentation of the communication network.

In some embodiments, the path, set of demands, and one or moretransceiver data types can be obtained from the same source. Forexample, a network controller or gateway may provide the path, set ofdemands, and transceiver data type(s). In various embodiments, the path,set of demands, and transceiver data type(s) can be obtained fromdifferent sources. For example, the computing device can be configuredwith network information describing a topology of the network (e.g.,nodes and edges, or the like). In some instances, the networkinformation can specify potential transceiver data type(s) for each nodeof the network. The computing device can then receive demands and pathinformation from one or more other computing devices (e.g., computingdevices associated with individual users). For example, a computingdevice of a user may request a connection between two nodes incommunication network 100. The request may indicate the nodes and ademand capacity associated with the connection. The computing device canaggregate such requests and use them to determine a service link set forsatisfying the demands.

In step 220 of method 200, the computing device can determine a segmentof the path (e.g., a segment of path 110). In some embodiments, thesegment of the path can be an initial segment of the path. For example,when the path proceeds from node N₁ through nodes N₂, N₃, and N₄ to nodeN₅ (e.g., as depicted in FIG. 1), the segment may be node N₁ and N₂, ornodes N₁ to N₃, or nodes N₁ to N₄, or nodes N₁ to N₅ (e.g., the entirepath). In some embodiments, the segment may be determined byconcatenating to a current segment the next segment in the path. Forexample, with reference to FIG. 1, when the current segment includesedges e₁ and e₂, the computing device can determine the next segment byadding edge e₃ to the current segment, or adding edges e₃ and e₄ to thecurrent segment (to yield the entire path).

In step 230, the computing device can determine a weight for each pathpair in the segment. Determining a weight for each path pair can includedetermining the potential path pairs for the segment. Each path pair caninclude an initial portion of the segment and a complementary portion ofthe segment. For example, with reference to FIG. 1, when the segmentincludes edges e₁, e₂, and e₃, then the path pairs can include:

path pair {p₁, p₂}, where p₁={e₁} and p₂={e₂,e₃}

path pair {p₃, p₄}, where p₃={e₁,e₂} and p₁={e₃}

The computing device can be configured to determine total weights forsub-paths p₁, p₂, p₃, and p₄. The total weights for a sub-path candepend on the set of service links for that sub-path.

In some embodiments, the total weight for a sub-path can be determinedusing a heuristic. In some instances, for example, the computing devicemay consider only sets of service links satisfying a criterion whendetermining a total weight for a sub-path. For example, the computingdevice may consider only sets of service links of a single transceiverdata type when determining a total weight for a sub-path. As anadditional or alternative criterion, the computing device may consideronly sets of service links that span the sub-path (e.g., service linksthat originate at the beginning of the sub-path and terminate at the endof the sub-path). In various embodiments, the computing device can useoptimization techniques such as integer linear programming (ILP) todetermine a total weight for a sub-path. The total weight for each pathpair can then be determined based on the total weights for eachsub-path. For example, the total weight for each path pair can be thesum of the total weights for the sub-paths.

As a non-limiting example of using a heuristic to determine a totalweight for a sub-path, the computing device may consider only sets ofservice links of a single transceiver data type that span the sub-path.Consistent with this approach, the computing device may determine a setof service links for each transceiver data type. Each set of servicelinks may have an associated weight. For example, the computing devicemay determine sets of service links SLS(P, D, TD), each with anassociated weight W(P, D, TD). TD can be one of the transceiver datatypes in TD-list, the set of possible transceiver data types, while Pcan be the sub-path and D can be the set of demands. The computingdevice may disregard or assign a default weight (e.g., a large orinfinite weight) to service links that do not span the path (e.g.,service links that originate or end in the middle of the sub-path). Thecomputing device may select the set of service links with the lowestassociated weight as the set of service links for the sub-path.

In some embodiments, the determination of SLS(P, D, TD) may beformulated as a bin-packing problem. The bin-packing problem can besolved using a greedy algorithm, or another algorithm adapted to solvingbin-packing problems. For example, the computing device can select ademand (arbitrarily or according to some decision rule). If an existingservice link has the capacity to accept the demand, then the demand canbe associated with this service link. If no existing service link hasthe capacity to accept the demand, then the computing device can createa new service link to accept the demand. This process can continue untilall demands are associated with a service link. The computing device maythen determine a total weight for the service link set based on theweights of the service links in the set (e.g., adding up the weights foreach service link in the service link set to obtain a total weight). Thecomputing device may determine a set of service links and an associatedtotal weight for each transceiver data type. The computing device maythen select the set of service links with the lowest weight as the setof service links for the sub-path.

As a non-limiting example of using an optimization technique todetermine a total weight for a sub-path, the computing device can useILP to determine which of a group of service link sets for a sub-pathhas the lowest weight. The group of service link sets may include allpossible service link sets of the sub-path, or only some of the servicelinks sets for the sub-path. For example, the group of service link setsmay include only those service links sets satisfying some criterion. TheILP optimization can be formulated as minimization of an objectivefunction c^(T)x such that Ax≤b, where x=(x₁, . . . , x_(n)) andx_(i∈{1, . . . , n}) is an integer. Depending on the complexity of theproblem (e.g., the number of edges in the sub-path, the number ofdemands, the number of different types of transceiver data types, thenumber or type of constraints, or the like) and the amount of computingresources available to the computing device (e.g., the processorspeed(s), number of processors/cores/threads, available memory,processing time, or the like), the computing device may be able todetermine a set of service links that minimizes the objective functionsubject to the constraints. In some embodiments, when the computingdevice is unable to determine such a set of service links (e.g., thecomputing device is unable to determine such a set using the allocatedprocessor time, memory, or the like), the computing device may assign adefault weight to the sub-path. This assigned weight may bepredetermined (e.g., a worst-case value or an infinite value, or thelike).

In some embodiments, the ILP objective function may be formulated as:min Σ_(i≤j)Σ_(TD)Σ_(k∈{1, . . . ,k) _(TD}) weight(TD)*x(TD,i,j,k)

where i is the first node in a section of the sub-path, j is the lastnode in the section of the sub-path, TD is a transceiver data-type, andthe set {1, . . . , k_(TD)} includes the service links of transceivertype TD connecting node i to node j.

In some embodiments, the ILP objective function can be maximized subjectto one or more of the following constraints:

Each demand d in the overall set of demands D may be satisfied by atmost one service link over each section of the sub-path (e.g., the samedemand cannot be allocated to multiple service links in the section).Accordingly:∀d∈D,∀i≤j,Σ _(TD)Σ_(k∈{1, . . . ,k) _(TD) _(}) y(d,TD,i,j,k)≤1

Each demand d is satisfied by exactly one service link that starts atthe first node in the path. Accordingly:∀d∈D,Σ _(TD)Σ_(k∈{1, . . . ,k) _(TD) _(})Σ_(j) y(d,TD,j,n,k)=1

Each demand d is satisfied by exactly one service link that ends at thelast node in the path. Accordingly:∀d∈D,Σ _(TD)Σ_(k∈{1, . . . ,k) _(TD) _(})Σ_(j) y(d,TD,j,n,k)=1

Each demand d is satisfied by the same number of service links thatstart at node i and end at node j. Accordingly:∀d∈D,∀i∉{0,n}Σ _(TD)Σ_(k∈{1, . . . ,k) _(TD) _(})Σ_(j<i)y(d,TD,j,i,k)−Σ_(TD)Σ_(k∈{1, . . . ,k) _(TD) _(})Σ_(j>j) y(d,TD,i,j,k)=0

Each service link has a capacity bound dependent on the transceiver datatype associated with that service link. The total of the demandcapacities for the demands associated with the service link is less thanthis capacity bound. Accordingly:∀_(TD) ∈TD−list,∀k∈{1, . . . ,k _(TD) },∀i≤j,Σ_(d∈D)capacity(d)*y(d,TD,i,j,k)≤capacity(TD)*x(TD,i,j,k)

Each service link has a maximum length dependent on the transceiver datatype associated with that service link. The total length of the sectionfrom node i to node j is less than this maximum length. Accordingly,∀_(TD) ∈TD−list,∀k∈{1, . . . ,k _(TD)},∀i≤j,length(TD)*x(TD,i,j,k)≥length(P _(i,j))*x(TD,i,j,k)

The computing device can be configured to determine a set of servicelinks that minimizes the object function subject to the constraints. Thecomputing device can be configured to determine this set of servicelinks using a solver such as CPLEX® Optimizer®, Modular In-coreNonlinear Optimization System (MINOS), COIN-OR Linear Programming (CLP),GNU Linear Programming Kit (GLPK), or the like. The disclosedembodiments are not limited to embodiments that identify a set ofservice links for a sub-path using the particular heuristic describedabove, or using ILP. Consistent with disclosed embodiments, thecomputing device may use other approaches to determining a set ofservice links for a sub-path, without limitation.

In step 240, the computing device can be configured to select a pathpair based on the total weights determined in step 230 for each pathpair in the segment. In some instances, the computing device can beconfigured to select the path pair having the lowest total weight. Suchselection can include, without limitation, storing (e.g., in a storagemedium of the computing device or accessible to the computing device, orthe like) at least one of the selected path pair or an indication of theselected path pair (e.g., a name, label, listing, pointer or referenceto the selected path pair or the sets of service links for the selectedpair, or the like). Such selection may further include, in someembodiments, storing (e.g., in a storage medium of the computing deviceor accessible to the computing device, or the like) at least one of thetotal weight of the selected path pair or an indication of the totalweight of the selected path pair (e.g., pointer or reference to thetotal weight, or the like).

In step 250, the computing device can determine whether the segment isequal to the overall path. When the segment is equal to the overallpath, then the selected path pair with the minimum total weight for thesegment can be the selected path pair with the minimum total weight forthe overall path. Method 200 can then proceed to step 260. When thesegment is a subset of the overall path, then method 200 can return tostep 220. As described above, in step 220 the computing device candetermine a new segment. This new segment can be, in some instances, anextension of the segment for which the path pairs were selected in step240.

In step 260, the computing device can be configured to select the pathpair for the segment as the path pair for the overall path. Suchselection can include, without limitation, storing, as the path pair forthe overall path, at least one of the selected path pair or anindication of the selected path pair (e.g., a name, label, listing,pointer or reference to the selected path pair or the sets of servicelinks for the selected pair, or the like). Such selection may furtherinclude, in some embodiments, storing at least one of the total weightof the selected path pair or an indication of the total weight of theselected path pair (e.g., pointer or reference to the total weight, orthe like).

In some embodiments, during or after step 260, the computing device canconfigure communication network 100 to use the sets of service links forthe selected path pair to satisfy the demands over the path. Forexample, the computing device can be configured to provide instructionsto switches, routers, transceiver-transponders, or the like of thecommunications network 100. The instructions can configure theseswitches, routers, transceiver-transponders, or the like to use theservice links for the selected path pair to satisfy the demands over thepath.

In some embodiments, rather than determining weights for each path pairin step 230, the computing device can be configured to determine totalweights for at least some sub-paths prior to step 230. These totalweights can be determined, in some instances, prior to determining thesegment in step 220. For example, the computing device can be configuredto determine such total weights as an initial step, after obtaining thepath, demands, and one or more transceiver data types in step 210.

FIG. 3 depicts exemplary selection of service links for the path 110from FIG. 1, consistent with disclosed embodiments. In the exampledepicted, selection of these service links occurs in four iterations. Inthis non-limiting example, sets of service links are determined forsub-paths using the heuristic approach outlined above with regards tostep 230 of FIG. 2.

In iteration 310 the segment can include a single edge (e.g., e₁), asshown. The segment can be divided into a null initial portion and acomplementary portion including the first edge, or an initial portionincluding the first edge and a null complementary portion. The weight ofa null initial or complementary portion can be deemed to be zero.

The computing device can determine a set of service links satisfying thedemands over the non-null initial or complementary portion for each ofthe transceiver data types (e.g., TD₁ and TD₂). The length of edge e₁ is800, so the length bounds associated with both TD₁ and TD₂ aresatisfied. Using a greedy algorithm that progressively assigns demandsto available service links, if possible, creating new service links ifnecessary, the following sets of service links can be identified:

SLS({e₁},{d₁,d₂,d₃},TD₁) can include a single service link satisfyingall of the demands, with an associated weight W({e₁},{d₁,d₂,d₃},TD₁)=17.SLS({e₁},{d₁,d₂,d₃},TD₂) can include two parallel service links, thefirst satisfying demands d₁ and d₂, the second satisfying demand d₃. Theassociated weight W({e₁},{d₁,d₂,d₃},TD₂)=2×13=26. As the weightassociated with SLS({e₁},{d₁,d₂,d₃},TD₁) is lower than the weightassociated with SLS({e₁},{d₁,d₂,d₃},TD₂), the computing device canselect SLS({e₁},{d₁,d₂,d₃},TD₁) as the set of service links for thesegment (e.g., as MinSLS(e₁)).

The disclosed embodiments are not limited to embodiments starting with asingle edge. In some embodiments, the determination can start with asegment including two or more edges (e.g., the determination can startwith the segment depicted in iteration 320).

In iteration 320, the segment can include two edges (e.g., e₁ and e₂).Two path pairs can be generated for this segment. A first path pair forthis segment can include a null portion (having a null weight) and acomplementary portion spanning two edges. A second path pair for thissegment can include an initial portion including edge e₁ and acomplementary portion including edge e₂.

The computing device can determine a total weight for the first pathpair. The null portion can have a weight of zero. The computing devicecan determine a set of service links (e.g., SLS(e₁,e₂)) and associatedweight for the complementary portion spanning two edges. The totallength of edges e₁ and e₂ is 1500, so the metric bound associated withTD₁ (e.g., 800) is not satisfied. Accordingly, the computing device maydisregard this service link set, or assign it a predetermined value(e.g., infinity). The computing device can identify a set of servicelinks SLS({e₁,e₂},{d₁,d₂,d₃},TD₂) that satisfy the demands using abin-packing algorithm, as described herein. This set of service linkscan include two parallel service links, the first satisfying demands d₁and d₂, the second satisfying demand d₃. The associated weightW({e₁,e₂},{d₁,d₂,d₃},TD₂)=2×13=26. As the null portion has a weight ofzero, the total weight for the first path pair can be 26.

The computing device can determine a total weight for the second pathpair. The lowest weight over edge e₁ was previously determined initeration 310 (e.g., the weight of 17 associated with MinSLS(e₁)). Thecomputing device can determine the set of service links with the lowestdetermined total weight that satisfies the demands over edge e₂ (e.g.,SLS(e₂)). The metric of edge e₂ is 700, so the metric bounds associatedwith both TD₁ and TD₂ are satisfied. The computing device can determinea set of service links and associated weights for each transceiver datatype:

SLS({e₂},{d₁,d₂,d₃},TD₁) can include a single service link satisfyingall of the demands, with an associated weight W({e₂},{d₁,d₂,d₃},TD₁)=17.SLS({e₂},{d₁,d₂,d₃},TD₂) can include two parallel service links, thefirst satisfying demands d₁ and d₂, the second satisfying demand d₃. Theassociated weight W({e₂},{d₁,d₂,d₃},TD₂)=2×13=26.

As the weight associated with SLS({e₂},{d₁,d₂,d₃},TD₁) is lower than theweight associated with SLS({e₂},{d₁,d₂,d₃},TD₂), the computing devicecan select SLS({e₂},{d₁,d₂,d₃},TD₁) as the set of service links with thelowest determined total weight that satisfies the demands over edge e₂(e.g., SLS(e₂)).

The total weight associated with the second path pair for the segmentcan be the sum of the weights associated with each sub-path (e.g.,W({e₁},{d₁,d₂,d₃},TD₁)+W({e₂},{d₁,d₂,d₃},TD)₁)=34).

As the total weight for first path pair (26) is less than the weight forthe second path pair (34), the computing device can select the firstpath pair as the set of service links for this segment (e.g., thecomputing device can select the first path pair as MinSLS(e₁,e₂)).

In iteration 330, the segment can include three edges (e.g., e₁,e₂, ande₃). Three path pairs can be generated for this segment. A first pathpair can include a null portion (having a null weight) and acomplementary portion spanning three edges. A second path pair caninclude an initial portion including edge e₁ and a complementary portionincluding edges e₂ and e₃. A third path pair can include an initialportion including edges e₁ and e₂ and a complementary portion includingedge e₃.

The computing device can determine a total weight for the first pathpair. The null portion can have a weight of zero. The total length ofthe complementary portion spanning edges e₁, e₂, and e₃ is 1900, so thelength bounds associated with TD₁ and TD₂ are not satisfied.Accordingly, the computing device may disregard the first path pair, orassign it a predetermined total weight (e.g., infinity).

The computing device can determine a total weight for the second pathpair. The lowest weight over edge e₁ was previously determined initeration 310 (e.g., the weight of 17 associated with MinSLS(e₁)). Thecomputing device can determine the set of service links with the lowestdetermined total weight that satisfies the demands over edges e₂ and e₃(e.g., SLS(e₂,e₃)). The total length of these edges is 1100, so only thelength bound associated with TD₂ is satisfied. The computing device candetermine a set of service links SLS({e₂,e₃},{d₂,d₂,d₃},TD₂) thatincludes two parallel service links that together satisfy the demands,with an associated weight W({e₂,e₃},{d₁,d₂,d₃},TD₂)=2×13=26. The totalweight associated with the second path pair for the segment can be thesum of the weights associated with each sub-path (e.g.,W({e₁},{d₁,d₂,d₃},TD₁)+W({e₂,e₃},{d₁,d₂,d₃},TD₂)=17+26=43).

The computing device can determine a total weight for the third pathpair. The lowest weight over edges e₁ and e₂ was previously determinedin iteration 320 (e.g., the weight of 26 associated with MinSLS(e₁,e₂)).The computing device can determine the set of service links with thelowest determined total weight that satisfies the demands over edge e₃(e.g., SLS(e₃)). The total length of this edge is 400, so the lengthbounds associated with TD₁ and TD₂ are both satisfied. The computingdevice can determine sets of service links for each of these transceiverdata types. As can be appreciated from the forgoing, the computingdevice can identify a set of service links SLS({e₃},{d₁,d₂,d₃},TD₁) thatincludes a single service link satisfying all of the demands as thelowest-weight set of service links. The associated weight can beW({e₃},{d₁,d₂,d₃},TD₁)=17. The total weight for the third path pair canbe the weights associated with each sub-path (e.g.,W({e₁,e₂},{d₁,d₂,d₃},TD₂)+W({e₃},{d₁,d₂,d₃},TD₂)=26+17=43).

The computing device may disregard the first path pair, as the totallength of the complementary segment exceeds the length bounds for bothtransceiver data types. As the total weight for second path pair (43)and the third path pairs (43) are equal, the computing device may selectone of these path pairs as the set of service links for this segment,randomly or according to some tie-breaking criterion. For example, thecomputing device can randomly select the second path pair as the set ofservice links for this segment (e.g., the computing device can selectthe second path pair as MinSLS(e₁,e₂,e₃)).

In iteration 340, the segment can include four edges (e.g., e₁,e₂,e₃,and e₄). Four path pairs can be generated for this segment. A first pathpair can include a null portion (having a null weight) and acomplementary portion spanning four edges. A second path pair caninclude an initial portion including edge et and a complementary portionincluding edges e₂, e₃, and e₄. A third path pair can include an initialportion including edges e₁ and e₂ and a complementary portion includingedges e₃ and e₄. A fourth path pair can include an initial portionincluding edges e₁, e₂, and e₃ and a complementary portion includingedge e₄.

The computing device can determine a total weight for the first pathpair. The null portion can have a weight of zero. The total length ofthe complementary portion spanning edges e₁, e₂, e₃, and e₄ is 2200, sothe length bounds associated with TD₁ and TD₂ are not satisfied.Accordingly, the computing device may disregard the first path pair, orassign it a predetermined total weight (e.g., infinity).

The computing device can determine a total weight for the second pathpair. The initial portion including edge e₁ can have the weightdetermined in iteration 310 (e.g., 17). The computing device candetermine the set of service links with the lowest determined totalweight that satisfies the demands over edges e₂, e₃, and e₄ (e.g.,SLS(e₂,e₃,e₄)). The total length of the complementary portion spanningedges e₂, e₃, and e₄ is 1400, so the length bound associated with TD₁ isnot satisfied. However, the length bound associated with transceiverdata type TD₂ is satisfied. As can be appreciated from the foregoing,the computing device can determine a set of service linksSLS({e₂,e₃,e₄},{d₂,d₂,d₃},TD₂) that includes two parallel service linksthat together satisfy the demands, with an associated weightW({e₂,e₃,e₄},{d₁,d₂,d₃},TD₂)=2×13=26. The total weight for the secondpath pair can then be the sum of the total weights for each sub-path(e.g., 43).

The computing device can determine a total weight for the third pathpair. The initial portion including edges e₁ and e₂ can have the weightdetermined in iteration 320 (e.g., 34). The computing device candetermine the set of service links with the lowest determined totalweight that satisfies the demands over edges e₃ and e₄ (e.g.,SLS(e₃,e₄)). The total length of the complementary portion spanningedges e₃ and e₄ is 700, so the length bounds associated with TD₁ and TD₂are satisfied. As can be appreciated from the foregoing, the computingdevice can determine a lowest-weight set of service linksSLS({e₃,e₄},{d₁,d₂,d₃},TD₁) that includes a single service link thatsatisfies the demands, with an associated weightW({e₃,e₄},{d₁,d₂,d₃},TD₁)=13. The total weight for the second path paircan then be the sum of the total weights for each sub-path (e.g., 47).

The computing device can determine a total weight for the fourth pathpair. The initial portion including edges e₁, e₂, and e₃ can have theweight determined in iteration 330 (e.g., 43). The computing device candetermine the set of service links with the lowest determined totalweight that satisfies the demands over edges e₄ (e.g., SLS(e₄)). Thetotal length of the complementary portion spanning edge e₄ is 300, sothe length bounds associated with TD₁ and TD₂ are satisfied. As can beappreciated from the foregoing, the computing device can determine alowest-weight set of service links SLS({e₃,e₄},{d₁,d₂,d₃},TD₁) thatincludes a single service link that satisfies the demands, with anassociated weight W({e₃,e₄},{d₁,d₂,d₃},TD₁)=13. The total weight for thesecond path pair can then be the sum of the total weights for eachsub-path (e.g., 56).

The computing device may disregard the first path pair, as the totallength of the complementary segment exceeds the length bounds for bothtransceiver data types. The total weight for second path pair is 43, thetotal weight for the third path pair is 47, and the total weight for thefourth path pair is 56. The computing device may therefore select thesecond path pair as the set of service links for this segment (e.g., thecomputing device can select the second path pair asMinSLS(e₁,e₂,e₃,e₄)).

The segment in iteration 340 is coterminous with the entire path. Thus,the second path pair is the set of service links with the lowestdetermined total weight that satisfy the demands over the entire path.This second path pair includes the set of service links with lowesttotal weight for edge et (e.g., SLS(e₁)) and the set of service linkswith the lowest total weight for edges e₂, e₃, and e₄ (e.g.,SLS(e₂,e₃,e₄)). Together, these sets of service links have the lowestdetermined total weight that satisfy the demands over the entire path.

As can be appreciated from the foregoing, the computing device can beconfigured to reuse, in later iterations, determinations made inprevious iterations. In some instances, once a set of service links hasbeen identified as having the lowest determined total weight over asub-path, the computing device can reuse that set of service linkswhenever the sub-path is encountered in subsequent iterations (e.g.,without re-determining or deriving that set of service links). Forexample, SLS({e₁},{d₁,d₂,d₃},TD₁) is identified as having the lowestdetermined total weight over sub-path e₁ in iteration 310. The computingdevice can then reuse that determination in iterations 320 to 340 whenevaluating the lowest determined total weight over the sub-path et.Likewise, the SLS({e₁,e₂},{d₁,d₂,d₃},TD₂) is identified as having thelowest determined total weight over the path including edges e₁ and e₂in iteration 320. The computing device can then reuse this determinationin iterations 330 and 340 when evaluating the lowest determined totalweight over the sub-path e₁,e₂. In this manner, method 200 can increasespeed and decrease the usage of computing resources by avoidingre-determination of the set of service links with the lowest determinedtotal weight for previously encountered sub-paths.

The foregoing example is not intended to be limiting. As describedabove, with regards to step 230 of FIG. 2, in some embodiments anoptimization techniques such as integer linear programming can be usedto determine a total weight for a sub-path. However, determination of alowest-weight set of service links over some paths (e.g., thoseincluding multiple edges) may be computationally infeasible.Accordingly, in such embodiments, the computing device may allocate acertain amount of computing resources (e.g., a certain amount of time,processing power, or the like) to determining the lowest-weight set ofservice links over a path. Should the allocated computing resources beexpended before determination of the lowest-weight set of service linksis complete, the computing device may associate the path with thelowest-total-weight set of service links so far identified (if any) ormay disregard the path pair including the path. The computing device mayproceed with determining weights for other path pairs. For example, withreference to iteration 340 of FIG. 3, the computing device may attemptto determine a set of service links for the complementary portionincluding edges e₁, e₂,e₃, and e₄. The computing device may be unable tocomplete this determination in an allocated time. The computing devicemay consequently associate the complementary portion with thelowest-weight set of service links identified in the allocated time, ormay disregard the path pair including this sub-path (e.g., the path pairincluding the empty sub-path and this complementary portion).

In some embodiments, as described herein, simplifying assumptions orheuristics may be used to determine a set of service links andcorresponding total weight for a path. The shorter the path (e.g., thefewer edges the path includes), the closer in total weight thedetermined set of service links may be to the optimal set of servicelinks (e.g., the set of service links satisfying the demands on the pathand having the lowest total weight for the path). Conversely, the longerthe path, the greater the deviation between the total weight for thedetermined set of service links and the total weight for the optimal setof service links. Accordingly, in some embodiments, the computing devicemay forego determining sets of service links for paths longer than somethreshold length. The particular threshold may depend on the network,transceiver data types, demands, or other factors and may be selected orempirically determined.

As a non-limiting example, a path on a communication network (e.g.,similar to path 110 on communications network 100) can include k edges,each edge having a metric value (e.g., length) of n. In this example,the path can be associated with demands {d₁,d₂,d₃,d₄}, each having ademand capacity of v. In this example, the communication network can beassociated with three transceiver data types:

TD₁ can have a capacity bound of 4v, a metric value bound of n, and aweight value of p.

TD₂ can have a capacity bound of 2v, a metric value bound of 2n, and aweight value of q.

TD₃ can have a capacity bound of v, a metric value bound of 3n, and aweight value of r.

In this non-limiting example, r<q<p and p<2q<4r.

A computing device can be configured to determine a set of service linksthat satisfy the demands over the path, in accordance with the examplesand methods described above with regards to FIGS. 1 to 3. The servicelinks selected by the computing device can depend on the relative valuesof the weights and the value of k.

In some instances, 4r>p+2q and k is even. In such instances, a computingdevice selecting service links in accordance with the examples andmethods described above with regards to FIGS. 1 to 3 may select, as theset of service links satisfying the demands on the communicationsnetwork, k service links of transceiver data type TD₂. The total weightassociated with the selected set of service links is then kq.

In some instances, 4r>p+2q and k is odd. In such instances, a computingdevice selecting service links in accordance with the examples andmethods described above with regards to FIGS. 1 to 3 may select, as theset of service links satisfying the demands on the communicationsnetwork, k−1 service links of transceiver data type TD₂ and one servicelink of transceiver data type TD₂. The total weight associated with theselected set of service links is then p+(k−1)q.

In some instances, 4r<p+2q and 4r>3q and k is even. In such instances, acomputing device selecting service links in accordance with the examplesand methods described above with regards to FIGS. 1 to 3 may select, asthe set of service links satisfying the demands on the communicationsnetwork, k service links of transceiver data type TD₂. The total weightassociated with the selected set of service links is then kq.

In some instances, 4r<p+2q and 4r>3q and k is odd but not equal to 1. Insuch instances, a computing device selecting service links in accordancewith the examples and methods described above with regards to FIGS. 1 to3 may select, as the set of service links satisfying the demands on thecommunications network, k−3 service links of transceiver data type TD₂and four service links of transceiver data type TD₃. The total weightassociated with the selected set of service links is then 4r+(k−3)q.

In some instances, 4r<p+2q and 4r>3q and k is equal to 1. In suchinstances, a computing device selecting service links in accordance withthe examples and methods described above with regards to FIGS. 1 to 3may select, as the set of service links satisfying the demands on thecommunications network, one service link of transceiver data type TD₁.The total weight associated with the selected set of service links isthen p.

In some instances, 4r<p+2q and p+4r<4q and k mod 3=0. In such instances,a computing device selecting service links in accordance with theexamples and methods described above with regards to FIGS. 1 to 3 mayselect, as the set of service links satisfying the demands on thecommunications network, 4k/3 service links of transceiver data type TD₃.The total weight associated with the selected set of service links isthen 4kr/3.

In some instances, 4r<p+2q and p+4r<4q and k mod 3=1. In such instances,a computing device selecting service links in accordance with theexamples and methods described above with regards to FIGS. 1 to 3 mayselect, as the set of service links satisfying the demands on thecommunications network, 4(k−1)/3 service links of transceiver data typeTD₃ and one service link of transceiver data type TD₁. The total weightassociated with the selected set of service links is then p+4(k−1)r/3.

In some instances, 4r<p+2q and p+4r<4q and k mod 3=2. In such instances,a computing device selecting service links in accordance with theexamples and methods described above with regards to FIGS. 1 to 3 mayselect, as the set of service links satisfying the demands on thecommunications network, 4(k−2)/3 service links of transceiver data typeTD₃ and two service links of transceiver data type TD₂. The total weightassociated with the selected set of service links is then 2q+4(k−2)r/3.

As would be appreciated by those of skill in the art, the forgoingexample describes a particular arrangement of edges, demands, andtransceiver data types, and is not intended to be limiting.

Service Link Decomposition

FIG. 4 depicts determination of a spanning subset of service links forexemplary communication network 100, consistent with disclosedembodiments. FIG. 4 depicts representation 400 of communication network100. As described herein, communication network 100 can be an opticalcommunication network (e.g., a fiber optic network), an electricalcommunication network (e.g., an ethernet or PSTN network), or a hybridnetwork including optical and electrical components. Representation 400comprises nodes (e.g., node 401) that are connected by edges (e.g., edge402). In some instances, depending on the communications network,representation 400 can be a graph, such as a cycle graph. As describedabove, a node can represent one or more signal-handling devices, whichmay or may not be geographically co-located. An edge can represent oneor more signal pathways connecting or potentially connecting two nodes.A set of service links can be associated with the communications network(e.g., service link 403). Each service link can be associated with apath (e.g., a set of edges on the communication network spanned by theservice link). Each service link may have a set of demands that use theservice link. As described herein, such demands can arise from userrequests for streaming video, videoconferencing applications, websurfing, or the like. The disclosed embodiments are not limited to anyparticular demand type or demand origin. Each demand can have a demandcapacity and each service link can have a capacity bound—e.g., the sumof the demand capacities for the demands satisfied by the service linkcannot exceed this capacity bound. In the example depicted in FIG. 4,service links l₁ to l₄ are associated with demands d₁ to d₄, each with ademand capacity of 20, service link l₅ is associated with a demand d₅with a demand capacity of 40, service link l₆ is associated with ademand d₆ with a demand capacity of 60, and service link l₇ isassociated with a demand d₇ with a demand capacity of 60. Each servicelink, in this non-limiting example, has a capacity bound of 100. Asdescribed above, the disclosed embodiments are not limited to aparticular measure of demand or capacity bound and the descriptionsprovided herein use unitless numbers for convenience of explanation.

A computing device associated with the communications network may beconfigured to determine a reduced subset of the service links that cansatisfy the demands. In some embodiments, this reduced subset maysatisfy the demands without violating any capacity bound or changing thepath of any service link. The reduced subset of service links can beachieved by “decomposing” service links (e.g., assigning the demandssatisfied by the service link to other service links). As a non-limitingexample, a service link l has a path p along a set of edges in thecommunication network. The service link l satisfies a demand d with ademand capacity x. Service links {l₁, . . . , l_(t)} have paths {p₁, . .. , p_(t)} and satisfy demands {d₁, . . . , d_(t)} with demandcapacities {x₁, . . . , x_(t)} and capacity bounds {m₁, . . . , m_(t)}.

Then dec(l)={l₁, . . . , l_(t)} is a decomposition of l when:

The concatenation of paths {p₁, . . . , p_(t)} equals p. As an exampleof such concatenation, concatenating the paths of l₁ and l₂ yields thepath of l₅, while concatenating service link l₄ with a service linkhaving a path from node n₂ to n₄ would not yield the path of l₆, as theresulting path would start at n₂, not n₃.

The service links {l₁, . . . , l_(t)} can satisfy demand d withoutexceeding their individual capacity bounds. As an example:Σ_(i∈s) x(i)≤m(i)

where S is the union of demands {d₁, . . . , d_(t)} and demand d, i is ademand in S, x(i) is the demand capacity of demand i, and m(i) is thecapacity bound of demand i.

The set of all possible decompositions of service link l is denotedDEC(l). As can be observed from the definition of decomposition, eachdemand can be decomposed into itself (e.g., the trivial decomposition).In some embodiments, DEC(l) includes the trivial decomposition.

In some embodiments, the decomposed service link can be removed from therepresentation of the communication network. In various embodiments,after determining the reduced subset of service links, the computingdevice or another device can provide instructions to the signal-handlingdevices represented by the nodes. These instructions can configure thenodes (and thus the communication network) to satisfy the demands usingthe reduced set of service links. For example, the instructions canconfigure the signal-handling devices to modify a service link tosatisfy additional demands, or tear down a decomposed service link.

Representation 410 depicts a spanning subset that is capable ofsatisfying all of the demands satisfied by representation 400, withoutrequiring as many service links. For example, where L={l₁, . . . ,l_(t)} is a set of service links having paths {p₁, . . . , p_(t)}, thenL′⊆L is a spanning subset of L when there exists a decompositiondec(l_(i)) for all l_(i)∈L that includes only service links in L and thecapacity bounds remain satisfied for all l_(i)∈L′ after reassignment ofdemands from the decomposed service links to the service links in L′. Asmay be appreciated from the foregoing, determining that eachdecomposition in a spanning subset is individually valid does notnecessarily imply that the spanning subset is valid. A service link mayreceive demands from multiple decomposed service links. These additionaldemands may collectively cause the service link to exceed its capacity,even when each additional demand does not individually cause the servicelink to exceed its capacity bound.

In representation 410, service links l₅ and l₆ have been decomposed intoservice links l₁ and l₂ and l₃ and l₄, respectively. Demand d₅ issatisfied by service links l₁ and l₂, while demand d₅ is satisfied byservice links l₃ and l₄. The sum of the demand capacities satisfied byl₁ and l₂ is 60, while the sum of the demand capacities satisfied byservice links l₃ and l₄ is 80. As these total demand capacities are lessthan the capacity bounds of links l₁ to l₄, the decomposition of linksis and l₆ depicted in representation 410 is valid. In contrast, in someembodiments, decomposing service link l₇ into service link l₆ wouldrequire service link l₆ to satisfy demands d₃ and d₄. However, servicelink l₆ has a capacity bound of 100, while the sum of the demandcapacities of demands d₃ and d₄ is 120. As the sum of the demandcapacities exceeds the capacity bound, the decomposition of l₇ intoservice links l₁, l₂, and l₆ would not be valid.

FIG. 5 depicts a method 500 for generating a spanning subset of servicelinks for a communication network, consistent with disclosedembodiments. In some embodiments, method 500 can include iterativelyprocessing a set of decompositions for a set of service links togenerate a spanning subset of the service links. In each iteration, theset of decompositions can be used to select service links for inclusionin the spanning subset and the set of decompositions can be updated. Insome embodiments, the selected service links may lack a non-trivialdecomposition in the set of decompositions. In various embodiments,updating the set of decompositions can include selecting a non-trivialdecomposition of a service link in the set of decompositions. The demandfor the selected service link can be re-allocated according to thenon-trivial decomposition. The set of decompositions can then be updatedto remove decompositions of the selected service link and decompositionsrendered invalid by the reallocation of demands. In some embodiments,the iterative processing of the set of decompositions can proceed untilthe set of decompositions is empty. The spanning subset may then includeservice links capable of satisfying the demands associated with theoriginal set of service links without changing any service link paths.In this manner, method 500 can be used to reduce the number of servicelinks required to satisfy the demands on communication network 100.Reducing the number of service links required to satisfy the demands oncommunication network 100 may improve the performance of communicationnetwork 100, whether by increasing the number of demands the network canhandle, making more efficient use of existing service links, or reducingthe computational or physical (e.g., equipment or the like) resourcesused to maintain communication network 100 or satisfy demands oncommunication network 100.

In step 501, a computing device can be configured to obtain a set ofpermissible decompositions for a set of service links associated withcommunication network 100. The computing device can be a physical device(e.g., a laptop, desktop, workstation, server, cluster, or the like) ora virtual device (e.g., a virtual machine, cloud computing environment,assortment of compute and memory resources, or the like). The computingdevice can be part of, or be co-located with, equipment implementingcommunication network 100. In various embodiments, the computing devicecan determine the set of permissible decompositions, receive the set ofpermissible decompositions from another computing device, or retrievethe set of permissible decompositions from a non-transitorycomputer-readable medium, such as a storage device or computer memory.The computing device can obtain the set of permissible decompositionsautomatically or in response to user input. In some embodiments, thecomputing device can obtain the set of permissible decompositionsrepeatedly, periodically, or according to a schedule; in response to anindication from the communication network; or the like.

In step 503, the computing device can be configured to update a spanningsubset. Updating the spanning subset may include adding service links tothe spanning subset. In some embodiments, the spanning subset may becreated as an empty set and then service links may be added to it. Invarious embodiments, one or more service links may be selected forinclusion in the spanning subset. The spanning subset may be createdincluding these selected one or more service links. In some embodiments,in step 503, the computing device can be configured to identify servicelinks in the set of decompositions that lack a non-trivial decomposition(e.g., basic service links). As described above, for such basic servicelinks, the only permissible decomposition may be the service linkitself. The computing device can be configured to add any suchidentified service links to the spanning subset.

In step 505, the computing device can be configured to update the set ofpermissible decompositions based on the spanning subset. Such updatingcan include removing from the set of permissible decompositions anydecompositions of service links in the spanning subset. For example,when the computing device identifies a service link as a basic servicelink (e.g., because the set of permissible decompositions includes onlya trivial decomposition of this service link), the computing device mayadd the service link to the spanning subset and remove the trivialdecomposition of the service link from the set of permissibledecompositions. The updating of the spanning subset and the set ofpermissible decompositions can occur in any order and can occur a singleoperation or multiple operations (e.g., step 505 can occur before step503, step 503 and step 505 can occur in a single operation, or thelike).

In step 507, the computing device can be configured to select one of thepermissible decompositions. This decomposition can be selected based onthe spanning subset. In some embodiments, the computing device canidentify decompositions in the set of permissible decompositions thatinclude only service links in the spanning subset. For example, withregard to FIG. 4, service link l₇ can be validly decomposed into threedecompositions:DEC(l ₇)={{l ₅ ,l ₃ ,l ₄ },{l ₁ ,l ₂ ,l ₃ ,l ₄ },{l ₇}}

In this example, service links l₁, l₂, l₃, and l₄ are basic servicelinks and l₅ is not. The computing device can then identify thedecomposition dec(l₇)={l₁,l₂,l₃,l₄} as including only basic servicelinks.

In some embodiments, the computing device can select one of theidentified decompositions (e.g., those including only basic servicelinks). When multiple decompositions are identified, the computingdevice can be configured to determine, for each of the multiple servicelinks (e.g., each “potential selection”), how many additionaldecompositions would be prevented by selecting that service link. Insome embodiments, the computing device can be configured to determine,for each potential selection, the number of decompositions that would beremoved from the set of permissible decompositions (e.g., “the number ofpotential removals”) due to violations of capacity constraints (e.g., asin step 509, below). In some embodiments, having determined the numberof potential removals for each potential selection, the computing devicecan select the potential selection having the smallest number ofpotential removals. In some embodiments, the computing device maysimulate one or more additional iterations of this process. As anexample of performing one additional iteration, the computing device maydetermine, for each potential selection, the service links available fordecomposition (e.g., the “second-order potential selections”). Thecomputing device can be configured to determine, for each combination ofa potential selection and a resulting second-order potential selection,the total number of decompositions that would be removed from the set ofpermissible decompositions. The computing device may select thepotential selection with the smallest total number of decompositions.

In step 509, the computing device can be configured to update the set ofpermissible decompositions based on the selected decomposition. In someembodiments, as detailed below with regard to FIG. 8, updating the setof permissible decompositions can include removing from the set ofpermissible decompositions any decomposition of the selected servicelink or including the selected service link. In various embodiments,updating the set of permissible decompositions can include updating thedemands associated with service links included in the selecteddecomposition. In some instances, these service links can becomeassociated with the demand formerly satisfied by the selected servicelink. This new association with the demand formerly satisfied by theselected service link can increase the demand capacity for these servicelinks. Accordingly, some of the remaining decompositions that includeservice links included in the decomposition of the selected service linkmay become invalid. Updating the set of permissible decompositions caninclude removing decompositions that violate capacity bounds based onthe updated demands.

In step 511, the computing device may determine whether the set ofpermissible decompositions is empty. When the set of permissibledecompositions is empty, the spanning set may be completely determinedand method 500 can proceed to providing the spanning set in step 513.When the set of permissible decompositions is not empty, the computingdevice may return to step 503 and update the spanning set. To continuethe prior example, service link l₅ now lacks a non-trivial decomposition(e.g., DEC(l₅)={{l₅}}). In the next iteration of method 500, servicelink l₅ may be added to the spanning subset in step 503 and the trivialdecomposition of service link l₅ may be removed from the set ofpermissible decompositions in step 505.

In step 513, the computing device can be configured to provide thespanning subset. Providing the spanning subset can include storing thespanning subset in a memory reachable by the computing device,displaying an indication of the spanning subset using a output deviceassociated with the computing device (e.g., an image or text displayedon computer display or printed by a printer, or the like); providing anindication of the spanning subset to another computing device; or thelike. In some embodiments, providing the spanning subset can includeconfiguring communication network 100 to satisfy the demands using theservice links in the spanning set. For example, the computing device canbe configured to directly or indirectly provide instructions to signalhandling devices implementing communication network 100 to configurethese devices to handle the demands using the service links in thespanning subset. The computing device may further provide instructions,directly or indirectly, to tear down or otherwise terminate servicelinks not included in the spanning subset.

FIGS. 6 and 7 depict a method 600 and associated decomposition graph 710for generating decompositions of a service link, consistent withdisclosed embodiments. In some embodiments, method 600 comprisesselecting a service link of a network (e.g., l₇ of FIG. 4), generating adecomposition graph for the service link (e.g., decomposition graph 710)and traversing the decomposition graph to generate the set of alldecompositions for the service link (e.g., the decomposition set DEC(l₇)for service link l₇). By formulating generation of the decomposition setas traversal of a decomposition graph, a flow algorithm can be used torapidly find multiple decompositions simultaneously. In someembodiments, the decompositions identified using the decomposition graphcan be used to determine a spanning subset, according to the method ofFIG. 5.

Method 600 can be performed by a computing device. The computing deviceof method 600 can be a physical device (e.g., a laptop, desktop,workstation, server, cluster, or the like) or a virtual device (e.g., avirtual machine, cloud computing environment, assortment of compute andmemory resources, or the like). This computing device can be part of, orbe co-located with, equipment implementing communication network 100. Invarious embodiments, the computing device 600 can be the same computingdevice described above with regards to method 500. In some embodiments,the computing device of method 600 can be distinct from the computingdevice of method 500. In such embodiments, the computing device ofmethod 600 can be configured to directly provide or indirectly provideservice link decompositions to the computing device of method 500. Forexample, the computing device of method 600 can be configured to storeor otherwise provide service links decompositions to a resource commonlyaccessible to the computing devices of methods 500 and 600.

In step 610 of method 600, the computing device can be configured toselect a service link from the set of service links associated withcommunications network 100. Selecting a service link can includeobtaining information concerning the service link (e.g., path, capacitybounds, demands, demand capacities, or the like) from one or moredevices implementing communications network 100. The computing devicecan be configured to select the service link randomly, or according to acriterion. For example, the computing device can be configured to selecta service link based on the length of the path for the service link, thecapacity bound of the service link, the demands or demand capacitiesassociated with the service link, or the like.

In step 620, the computing device can be configured to identify verticesin a decomposition graph for the service link. The decomposition graphcan be a directed graph with vertices V={V₁, . . . , V_(n)} and edgesE={(V₁, V_(j∈V\V) ₁ ), . . . }. An exemplary decomposition graph 710 forservice link l₇ of FIG. 4 is depicted in FIG. 7. In some instances, thevertices can represent paths through communication network 100. Forexample, where L={L₁, . . . , L_(k)} is the set of service links in thecommunication network 100, the service links having corresponding pathsP={P₁, . . . , P_(k)}:V _(j) ={P _(j) |∃P′⊂P and P′·P _(j) =P}

Accordingly, a path P_(j) in communication network 100 is a vertex inthe decomposition graph of a service link when the path of the servicelink can be decomposed into a prefix and a suffix, the path P_(j) beingthe suffix and the prefix being the concatenation of a subset P′ of thepaths in P. In some embodiments, the decomposition graph always includesthe path of the decomposed service link, as the concatenation of thenull path (as the prefix) and the path of the service link (as thesuffix) always equals the path of the service link. In some embodiments,the decomposition graph always includes the null path, as theconcatenation of the null path (as the suffix) and the path of theservice link (as the prefix) always equals the path of the service link.

As depicted in FIG. 7, decomposition graph 710 includes vertex 715(corresponding to the path of service link l₇) and vertex 711(corresponding to the null path). Decomposition graph 710 furtherincludes vertex 712, with path P_(j)={e₄} and subset P′={e₁,e₂,e₃};vertex 713, with path P_(j)={e₃,e₄} and subset P′={e₁,e₂}; and vertex714, with path P_(j)={e₂,e₃,e₄} and subset P′={e₁}.

In step 630, the computing device can be configured to identify edges inthe decomposition graph for the service link. In this non-limitingexample, nodes are described as being found before edges. This orderingis not intended to be limiting. In some embodiments, for example, thedecomposition graph can be built through an iterative process of addingnodes or edges. In some instances, the computing device can identify anedge as connecting a first vertex to a second vertex when a pathassociated with a service link in communication network 100 is therelative complement of the second vertex with respect to the firstvertex. For example:E={(V _(i) ,V _(j))|∃l _(k) ∈L with P _(k) ∈P:P _(k) ·P _(j) =P _(i)}

In various embodiments, the computing device can further require thatthe service link satisfy a capacity bound criterion. For example, thecomputing device can require that the sum of the demand capacities forany demands associated with the identified service link and the servicelink being decomposed is less than the capacity bound for the identifiedservice link. For example:E={(V _(i) ,V _(j))|∃l _(k) ∈L:P _(k) ·P _(j) =P _(i) and x _(k) +x _(d)≤m _(k)}

Where l_(k) is a service link on communication network 100 associatedwith a demand d_(k) having a demand capacity x_(k), the service linkl_(d) for which the decomposition graph is being constructed isassociated with a demand d having a demand capacity x_(d), and thecapacity bound of the service link l_(k) is m_(k).

In some embodiments, the decomposition graph always includes an edgeconnecting the vertex corresponding to the path of the service linkbeing decomposed and the vertex corresponding to the null path, as thepath of the service link being decomposed is the relative complement ofthese two vertices and the service link being decomposed is capable ofsatisfying its own demand.

As depicted in FIG. 7, decomposition graph 710 includes edge 726 thatconnects vertex 715 (corresponding to the path of the service link) tovertex 711 (corresponding to the null path). In this non-limitingexample, the computing device can also determine that service link l₁has a path {e₁} that is the relative complement of vertex 714 withrespect to vertex 715. Furthermore, service link l₁ is associated with ademand d₁ having a demand capacity of 20 and service link l₇ (theservice link being decomposed) is associated with a demand d₇ having ademand capacity of 60. The capacity bound of service link l₁ is 100.Accordingly, the computing device can identify edge 721 as a valid edgein decomposition graph 710. To continue this example, the computingdevice can further determine that service link l₅ has a path {e₁,e₂}that is the relative complement of vertex 713 with respect to vertex715. Furthermore, service link l₅ is associated with a demand d₁ havinga demand capacity of 40, while service link l₇ is associated with ademand d₇ having a demand capacity of 60. The capacity bound of servicelink l₅ is 100. Accordingly, the computing device can identify edge 722as a valid edge in decomposition graph 710. In a similar manner, thecomputer device can identify edges 723, 724 and 725 as valid edges indecomposition graph 710.

The computing device can determine that no service link has a path thatis the relative complement of vertex 712 with respect to vertex 714.Accordingly, the computing device can determine that no edge connectsvertices 714 and 712. The computing device can also determine that noservice link with a sufficiently large capacity bound connects vertices713 and 711. Though service link l₆ has a path {e₂,e₃} that is therelative complement of vertex 711 with respect to vertex 713, thisservice link lacks sufficient capacity to satisfy its own demand and thedemand associated with service link l₇. Service link l₆ is associatedwith demand d₆, which has a demand capacity of 60 and a capacity boundof 100. In this non-limiting example, the decomposed service link l₇ isassociated with demand d₇, which has a demand capacity of 60. As the sumof the demand capacities for demands d₆ and d₇ (120) exceeds thecapacity bound of service link l₆ (100), service link l₆ cannot supportan edge connecting vertex 713 and vertex 711. As no other service linkis the relative complement of vertex 711 with respect to vertex 713, thecomputing device can determine that no edge connects vertex 713 andvertex 711.

In step 640, the computing device can use the decomposition graphgenerated for a service link to generate a set of decompositions forthat service link. The disclosed embodiments are not limited to aparticular method of generating a set of decompositions from thedecomposition graph. In some embodiments, the computing device cangenerate the set of decompositions by determining paths in thedecomposition graph. To determine paths in the decomposition graph, thecomputing device can use a maximal flow algorithm to find a maximalnumber of edge disjoint paths. Alternatively or additionally, thecomputing device can use an iteratively use a shortest path algorithm(for example Dijkstra) to determine the shortest path, then exclude(remove) an edge on the shortest path from the graph. The computingdevice can continue to iterate (e.g., find shortest path, remove edge onshortest path) until a path cannot be found. These paths can start atthe vertex corresponding to the decomposed service link (e.g., vertex715 in FIG. 7) and can end at the vertex corresponding to the null path(e.g., vertex 711 in FIG. 7). As described herein, each of the edges inthe decomposition graph is associated with a service link incommunication network 100. The service links associated with the edgesin a path from the vertex corresponding to the decomposed service linkto the vertex corresponding to the null path form a valid decompositionof the service link. For example, the computing device can identify apath from vertex 715 to vertex 711 along DEC 731 in decomposition graph710. The service links associated with this path are l₁ (associated withedge 721), l₂ (associated with edge 723), l₃ (associated with edge 724),and l₄ (associated with edge 725). Accordingly, the set {l₁,l₂,l₃,l₄}forms a valid decomposition of l₇. As an additional example, thecomputing device can identify a path from vertex 715 to vertex 711 alongDEC 733 in decomposition graph 710. The service links associated withthis path are is (associated with edge 722), l₃, and l₄. Accordingly,the set {l₅,l₃,l₄} forms a valid decomposition of l₇. As a furtherexample, the computing device can identify a path from vertex 715 tovertex 711 along DEC 735 in decomposition graph 710. The service linkassociated with this path is l₇ (associated with edge 726). Accordingly,the set {l₇} forms a valid decomposition of l₇ (the trivialdecomposition). As Dec 731, Dec 733, and Dec 735 are the only pathsthrough decomposition graph 710 from vertex 715 to vertex 711, the setsof service links associated with these sets of paths form the set ofdecompositions for l₇ (e.g., DEC(l₇)={{l₁,l₂,l₃,l₄},{l₅,l₃,l₄},{l₇}}).

FIG. 8 depicts an exemplary method 800 of updating a set of permissibledecompositions, consistent with disclosed embodiments. Method 800 canupdate the set of permissible decompositions in response to selection ofa decomposition of a service link. For example, in some embodiments,method 800 can be performed as part of method 500. Method 800 can beperformed by the same computing device as method 500, or anothercomputing device. The computing device configured to perform method 800can be separate or apart from, or co-located with, devices implementingcommunications network 100.

As described herein, in method 800, the computing device can select adecomposition (e.g., the “selected decomposition”) of a service link(e.g. the “decomposed service link”). In step 810, the computing devicecan remove other decompositions of the decomposed service link, or otherdecompositions including the decomposed service link, from the set ofpermissible decompositions. In some embodiments, the computing devicecan remove all such decompositions from the set of permissibledecompositions. To continue the example in FIG. 5, after selectingdec(l₇)={l₁,l₂,l₃,l₄}, the computing device can remove from the set ofpermissible service links all other decompositions of service link l₇ orincluding service link l₇.

In step 820, the computing device can update the demands associated withthe service links included in the selected decomposition. In someembodiments, updating these demands can include associating with theseservice links the demand(s) previously associated with the decomposedservice link (the “decomposed service link demand(s)”). As thedecomposed service link demand(s) have demand capacities, updating theupdate the demands associated with the service links will increase thedemand capacities of these service links. To continue the example fromFIG. 5, service link l₇ may be associated with a demand d₇ having ademand capacity x₇. In step 820, in response to selection of thedecomposition of 17 into service links l₁ to l₄, the computing devicemay associate demand d₇ with each of service links l₁ to l₄. Servicelinks l₁ to 1₄ may originally have demands d₁ to d₄ with demandcapacities x₁ to x₄. Following association with demand d₇, service linksl₁ to l₄ may have demands {d₁,d₇} to {d₄,d₇} and total demand capacitiesx₁+x₇ to x₄+x₇. The validity of this reallocation of demands followsfrom the definition of a decomposition.

In step 830, the computing device can be configured to removedecompositions that violate capacity constraints based on the updateddemands. These other decompositions may include one or more of theservice links included in the selected decomposition. The decomposedservice link demand(s) associated with these service links may causethese other decompositions to become invalid. To continue the priorexample, the set of permissible decompositions may also include:DEC(l ₅)={{l ₁ ,l ₂ },{l ₅}}

Before, during, or after reallocating demand d₇ to service links l₁ andl₂, the computing device may determine that dec(l₅)={l₁,l₂} is no longera valid decomposition of l₅. In some embodiments, as described herein,dec(l₅) is a valid decomposition of l₅ when the sums of the demandcapacities for the demands associated with each of l₁ and l₂ are lessthan capacity bounds for each of l₁ and l₂. However, followingdecomposition of service link l₇, the demand capacities associated witheach of l₁ and l₂ have increased (e.g., from x₁ and x₂ to x₁+x₇ andx₂+x₇, respectively). Accordingly, the computing device may determinethat reallocating demand d₅ to service links l₁ and l₂ is no longer bepossible. The computing device may therefore remove dec(l₅)={l₁,l₂} fromthe set of permissible declarations. Accordingly, the set of alldecompositions for service link l₅ may become:DEC(l ₅)={{l ₅}}

In this example, not only did decomposed service link demand d₇ causedec(l₅)={l₁,l₂} to become invalid, the removal of dec(l₅)={l₁,l₂} fromDEC(l₅) caused service link l₅ to become a basic service link, as theonly decomposition of l₅ remaining in DEC(l₅) is the trivialdecomposition.

FIGS. 9A and 9B depicts determination of a spanning subset of servicelinks for a communications network 900 (e.g., a communications networkimplemented similar to communications network 100) represented by anexemplary cycle graph, consistent with disclosed embodiments. Each ofthe service links depicted in FIGS. 9A and 9B can have a capacity boundof 100. FIG. 9A depicts a communications network 900 including 24 nodesthis non-limiting example. Service links in a first group of servicelinks each traverse a single edge to connect adjacent nodes incommunications network 900 (e.g., first service links 910). The firstgroup of service links can include 24 service links. These service linksmay each have a demand with a demand capacity of 50.

Service links in a second group of service links each traverse two edges(e.g., second service links 920). These service links can be arranged intwo sub-sets. These service links can be staggered, with the servicelinks in one subset originating at nodes skipped by the service links inthe other sub-set. The second group of service links can include 24service links. These service links may each have a demand with a demandcapacity of 25.

Service links in a third group of service links each traverse threeedges (e.g., third service links 930). The third group of service linkscan include 8 service links. These service links may each have a demandwith a demand capacity of 50.

Consistent with method 500, a computing device can be configured toobtain decompositions of the service links in the first, second andthird groups. FIG. 9B depicts these decompositions. The service links inthe first group may have only the trivial decomposition. The servicelinks in the second group may be decomposable into either a pair ofservice links in the first group or the trivial decomposition. Theservice links in the third group may be decomposable into a first pairof service links including one of the second group of service linksconcatenated with one of the first group of service links, a second pairof service links including one of the first group of service linksconcatenated with one of the second group of service links, or thetrivial decomposition.

The computing device can determine that the initial set of basic servicelinks includes first service links 910. The device can then determinethat each of second service links 920 can be decomposed into servicelinks in the set of basic service links (e.g., each of second servicelinks 920 can be decomposed into two of first service links 910).Individually, or in a single iteration, the computing device can beconfigured to decompose the second service links into the first servicelinks, as described above with regards to FIGS. 5 and 8. As each of thesecond service links 920 is decomposed, the decomposition of thisservice link and all of decompositions including this service link canbe removed from the set of permissible decompositions. As can beappreciated from FIG. 9A, two service links in the second service links920 will be decomposed into each of first service links 910.Accordingly, the demands associated with two of the second service linkswill be reassigned to each of first service links 910. Thisdecomposition is valid, as the sum of demand capacities for all thedemands associated with each of the second service links followingreassignment (50+25+25) is still less than the capacity bounds of eachof the first service links 910.

However, the computing device can determine (e.g., before, during, orafter decomposing the second service links 920 into the first servicelinks 910) that the non-trivial decompositions of each of the thirdservice links 930 into pairs of one of the first service links 910 andone of the second service links 920 are no longer valid. As the firstservice links are now associated with total demand capacities of 100,the demands associated with the third service links 930 can no longer beassigned to the first service links 910 without violating the capacitybounds for these service links.

In some embodiments, the computing device can determine whetherdecomposing the third service links or decomposing the second servicelinks results in a smaller spanning subset. The computing device candetermine that decomposing each of the service links in the thirdservice links 930 prevents decomposition of 4 service links in thesecond service links 920, as reassigning the demands for the one of thethird service links 930 prevents any further decomposition of thecorresponding second service link 920 (as it would now have a totaldemand capacity of 75) or corresponding first service link 910 (as itwould now have a total demand capacity of 100). In constant, decomposingeach of the service links in the second service links 920 prevents onlythe decomposition of one service link of third service links 930.Accordingly, the computing device can determine that decomposing thesecond service links 920 results in a smaller spanning subset and selectthese service links for decomposition.

In various embodiments, the computing device (or another computingdevice) can be configured to provide instructions to computing network900 to satisfy the demands on the first, second, and third service linksusing only the first and third service links. In this manner, thecomputing device can reduce the number of service links used to satisfythe demands from 56 service links to 32 service links, therebypotentially improving the efficiency and flexibility of communicationsnetwork 900.

The foregoing description has been presented for purposes ofillustration. It is not exhaustive and is not limited to precise formsor embodiments disclosed. Modifications and adaptations of theembodiments will be apparent from consideration of the specification andpractice of the disclosed embodiments. For example, the describedimplementations include hardware, but systems and methods consistentwith the present disclosure can be implemented with hardware andsoftware. In addition, while certain components have been described asbeing coupled to one another, such components may be integrated with oneanother or distributed in any suitable fashion.

Moreover, while illustrative embodiments have been described herein, thescope includes any and all embodiments having equivalent elements,modifications, omissions, combinations (e.g., of aspects across variousembodiments), adaptations or alterations based on the presentdisclosure. The elements in the claims are to be interpreted broadlybased on the language employed in the claims and not limited to examplesdescribed in the present specification or during the prosecution of theapplication, which examples are to be construed as nonexclusive.Further, the steps of the disclosed methods can be modified in anymanner, including reordering steps or inserting or deleting steps.

The features and advantages of the disclosure are apparent from thedetailed specification, and thus, it is intended that the appendedclaims cover all systems and methods falling within the true spirit andscope of the disclosure. As used herein, the indefinite articles “a” and“an” mean “one or more.” Similarly, the use of a plural term does notnecessarily denote a plurality unless it is unambiguous in the givencontext. Further, since numerous modifications and variations willreadily occur from studying the present disclosure, it is not desired tolimit the disclosure to the exact construction and operation illustratedand described, and accordingly, all suitable modifications andequivalents may be resorted to, falling within the scope of thedisclosure.

As used herein, unless specifically stated otherwise, the term “or”encompasses all possible combinations, except where infeasible. Forexample, if it is stated that a component may include A or B, then,unless specifically stated otherwise or infeasible, the component mayinclude A, or B, or A and B. As a second example, if it is stated that acomponent may include A, B, or C, then, unless specifically statedotherwise or infeasible, the component may include A, or B, or C, or Aand B, or A and C, or B and C, or A and B and C.

The embodiments may further be described using the following clauses:

1. A method for determining a spanning subset of service links for acommunications network, comprising: obtaining a set of permissibleservice link decompositions for the communications network and a set ofbasic service links for the communications network; and generating thespanning subset, the generation including: selecting a decomposition ofa first service link from the set of permissible service linkdecompositions; updating the set of permissible service linkdecompositions based on the selected decomposition; and updating the setof basic service links using the updated set of permissible service linkdecompositions.

2. The method of clause 1, wherein: selecting the decomposition of thefirst service link comprises: determining that the decompositionincludes only service links in the set of basic service links; andselecting the decomposition in response to the determination.

3. The method of any one of clauses 1 to 2, wherein: the first servicelink is associated with a first demand; and updating the set ofpermissible service link decompositions based on the selecteddecomposition comprises: removing, from the set of permissible servicelink decompositions, decompositions of the first service link orincluding the first service link; updating demands associated withservice links included in the selected decomposition using the firstdemand; and removing decompositions that, based on the updated demands,violate a capacity constraint.

4. The method of any one of clauses 1 to 2, wherein: updating the set ofpermissible service link decompositions comprises removingdecompositions violating a capacity constraint from the set ofpermissible service link decompositions.

5. The method of any one of clauses 1 to 4, wherein: updating the set ofbasic service links using the updated set of permissible service linkdecompositions comprises: determining that the updated set ofpermissible service link decompositions lacks a non-trivialdecomposition of a second service link; and adding the second servicelink to the set of basic service links in response to the determination.

6. The method of any one of clauses 1 to 4, wherein: the set of basicservice links is updated to include ones of the service links lackingnon-trivial decompositions in the updated set of permissible servicelink decompositions.

7. The method of any one of clauses 1 to 6, wherein: generation of thespanning subset further includes: updating the set of permissibleservice link decompositions based on the updated set of basic servicelinks.

8. The method of any one of clauses 1 to 7, wherein: obtaining the setof permissible service link decompositions comprises: generating a setof permissible service link decompositions for each one of the servicelinks, the generation comprising: selecting a subset of the servicelinks based on a path of the each one of the service links and a firstdemand; generating a decomposition graph using the subset of the servicelinks; and generating the set of permissible service link decompositionsfor the each one of the services links using the decomposition graph.

9. The method of any one of clauses 1 to 7, wherein: obtaining the setof permissible service link decompositions comprises generating andtraversing a decomposition graph for each of the service links.

10. The method of any one of clauses 1 to 9, wherein: the method furthercomprises configuring the communications network to transmit networktraffic using the spanning subset of service links.

11. A method for configuring a communications network, comprising:obtaining a set of permissible decompositions of a set of service linksfor the communications network; iteratively determining a spanningsubset of the set of service links, an iteration comprising: updatingthe spanning subset of the set of service links based on the set ofpermissible service link decompositions; updating the set of permissibleservice link decompositions based on the spanning subset; selecting,from the set of permissible service link decompositions, a decompositionof a first service link; and updating the set of permissible servicelink decompositions using a first demand associated with the firstservice link; and configuring the communications network to transmitnetwork traffic using the spanning subset of service links.

12. The method of clause 11, wherein: selecting the decomposition of thefirst service link comprises: determining that the decompositionconsists of service links in the spanning subset; and selecting thedecomposition, at least in part, in response to the determination.

13. The method of any one of clauses 11 to 12, wherein: selecting thedecomposition of the service link further comprises: determining that noother decomposition consisting of service links in the spanning subsetincludes more service links than the selected decomposition.

14. The method of any one of clauses 11 to 13, wherein: updating the setof permissible service link decompositions based on the selecteddecomposition comprises: removing, from the set of permissible servicelink decompositions, decompositions of the first service link orincluding the first service link; updating demands associated withservice links included in the selected decomposition using the firstdemand; and removing decompositions that, based on the updated demands,violate a capacity constraint.

15. The method of any one of clauses 11 to 13, wherein: updating the setof permissible service link decompositions comprises removingdecompositions violating a capacity constraint from the set ofpermissible service link decompositions.

16. The method of any one of clauses 11 to 15, wherein: updating thespanning subset using the updated set of permissible service linkdecompositions comprises: determining that the updated set ofpermissible service link decompositions lacks a non-trivialdecomposition of a second service link; and adding the second servicelink to the spanning subset in response to the determination.

17. The method of any one of clauses 11 to 15, wherein: the spanningsubset is updated to consist of service links lacking non-trivialdecompositions in the updated set of permissible service linkdecompositions.

18. The method of any one of clauses 11 to 17, wherein: obtaining theset of permissible service link decompositions comprises: generating aset of permissible service link decompositions for the first servicelink, the generation comprising: selecting a subset of the service linksbased on a path of the first service link and the first demand;generating a decomposition graph using the selected subset of theservice links; and generating the set of permissible service linkdecompositions for the first service link using the decomposition graph.

19. The method of any one of clauses 11 to 17, wherein: obtaining theset of permissible service link decompositions comprises generating andtraversing a decomposition graph for each of the service links.

20. The method of any one of clauses 11 to 19, wherein: thedecomposition graph is traversed using a shortest path algorithm.

21. A method for configuring a communication network, comprising:determining a set of service links for a path in the communicationnetwork based on a set of demands for the path, the determinationcomprising: repeatedly selecting sets of service links for segments ofthe path, a repeat for a segment comprising: determining pair weightsfor path pairs, each path pair comprising: an initial portion of thesegment, the initial portion being associated with a first set ofservice links and a first weight dependent on the first set; acomplementary portion of the segment, the complementary portion beingassociated with a second set of service links and a second weightdependent on the second set; and wherein the pair weight for the eachpath pair depends on the first weight and the second weight; selecting apath pair for the segment based on the pair weight for the selected pathpair; and selecting the first and second sets of service links for theselected path pair as the set of service links for the segment; anddetermining, when the segment comprises the path, the set of servicelinks for the segment as the set of service links for the path; andconfiguring the communication network to service the set of demands forthe path using the selected set of service links for the path.

22. The method of clause 21, wherein: repeatedly determining the sets ofservice links for the segments of the path comprises iterativelydetermining the sets of service links for progressively longer initialsegments of the path.

23. The method of any one of clauses 21 to 22, wherein: the methodfurther comprises: selecting the second set of service links based on: ametric value associated with the complementary portion of the segmentand the set of demands; and transceiver data types specifying capacitybounds, metric value bounds, and weights for differing types of servicelinks; and wherein the second weight further depends on the weights forthe differing types of service links.

24. The method of clause 23, wherein: selection of the second set ofservice links is constrained by a requirement that each service link inthe second set spans the complementary portion of the segment.

25. The method of any one of clauses 23 to 24, wherein: a greedyselection algorithm is used to select the second set of service links.

26. The method of any one of clauses 23 to 25, wherein: the second setof service links is selected to minimize the second weight.

27. The method of clause 23, wherein: selecting the second set ofservice links comprises solving an integer linear programming problemincluding constraints dependent on the set of demands, the capacitybounds, the metric value associated with the complementary portion ofthe segment, and the metric value bounds.

28. The method of any one of clauses 21 to 27, wherein: the initialportion was a segment in a prior repeat; and the first set of servicelinks was the selected set of service links for the segment in the priorrepeat.

29. The method of any one of clauses 21 to 28, wherein: each demand inthe set of demands is associated with a subset of the service links, aunion of the service links in the subset being associated with the eachdemand spanning the path; and each service link in the set of servicelinks is associated with a subset of the demands, a sum of volumes ofthe demands in the subset associated with the each service link beingless than a capacity bound of the each service link.

30. The method of any one of clauses 21 to 29, wherein: the pathcomprises a sequence of edges; and each segment of the path comprises anumber of the initial edges in the sequence, the number incrementingwith each repeat.

31. The method of any one of clauses 21 to 30, wherein: the path pairfor the segment is selected to minimize a weight for the segment.

32. A method for determining a configuration of a communication network,comprising: obtaining, for a communication network comprising fiberoptic cables connected by switches and transceiver-transponders, arepresentation of the communication network as a set of edgesrepresenting the fiber optic cables, the edges connected by nodesrepresenting the switches and transceiver-transponders; and determininga set of service links for a path in the communication network based ona set of demands for the path, each service link representing datatransmission by one of the transceiver-transponders through one or moreof the fiber optic cables connected by zero or more of the switches, thedetermination comprising: iteratively selecting sets of service linksfor progressively longer initial segments of the path, an iteration foran initial segment comprising: determining pair weights for path pairs,each path pair comprising: an initial portion of the initial segment,the initial portion being associated with a first set of service linksand a first weight dependent on the first set; a complementary portionof the initial segment, the complementary portion being associated witha second set of service links and a second weight dependent on thesecond set; and wherein the pair weight for the each path pair dependson the first weight and the second weight; selecting a path pair for theinitial segment based on the pair weight for the selected path pair; andselecting the first and second sets of service links for the selectedpath pair as the set of service links for the initial segment; anddetermining, when the initial segment comprises the path, the set ofservice links for the initial segment as the set of service links forthe path.

33. The method of clause 32, wherein: the path comprises a sequence ofedges in the communication network; and each initial segment of the pathcomprises a number of the initial edges in the sequence, the numberincrementing with each iteration.

34. The method of any one of clauses 32 to 33, wherein: the methodfurther comprises:

selecting the second set of service links based on: a metric valueassociated with the complementary portion of the initial segment and theset of demands; and transceiver data types specifying capacity bounds,metric value bounds, and weights for differing types of service links;and wherein the second weight further depends on the weights for thediffering types of service links.

35. The method of clause 34, wherein: selection of the second set ofservice links is constrained by a requirement that each service link inthe second set span the complementary portion of the initial segment.

36. The method of any one of clauses 34 to 35, wherein: a greedyselection algorithm is used to select the second set of service links.

37. The method of any one of clauses 34 to 36, wherein: the second setof service links is selected to minimize the second weight.

38. The method of clause 34, wherein: selecting the second set ofservice links comprises solving an integer linear programming problemincluding constraints dependent on the set of demands, the capacitybounds, the metric value associated with the complementary portion ofthe initial segment, and the metric value bounds.

39. The method of any one of clauses 32 to 38, wherein: the initialportion was an initial segment in a prior repeat; and the first set ofservice links was the selected set of service links for the initialsegment in the prior repeat.

40. The method of any one of clauses 32 to 39, wherein: each demand inthe set of demands is associated with a subset of the service links, aunion of the service links in the subset being associated with eachdemand spanning the path; and each service link in the set of servicelinks is associated with a subset of the demands, a sum of volumes ofthe demands in the subset associated with each service link less beingthan a capacity bound of the each service link.

41. The method of any one of clauses 32 to 40, wherein: the methodfurther comprises configuring the communication network to service theset of demands for the path using the selected set of service links forthe path.

42. The method of any one of clauses 32 to 41, wherein: the path pairfor the initial segment is selected to minimize a weight for thesegment.

43. A method for determining a spanning set of service links for acommunications network, comprising: obtaining a set of service links fora cycle graph representing a communications network, wherein the set ofservice links comprises: a first subset of first service links, each ofthe first service links traversing at most a first number of edges inthe cycle graph and associated with one of first demands having a firstdemand capacity; a second subset of second service links, each of thesecond service links traversing at most a second number of edges in thecycle graph and associated with one of second demands having a seconddemand capacity; a third subset of third service links, each of thethird service links traversing at least a third number of edges in thecycle graph and associated with one of third demands having a thirddemand capacity; and wherein a first capacity bound of the first servicelinks is greater than or equal to the sum of the first demand capacityand two times the second demand capacity; wherein the first capacitybound of the first service links is greater than or equal to the sum ofthe first demand capacity and the third demand capacity; and wherein thefirst capacity bound of the first service links is less than the sum ofthe first demand capacity, the second demand capacity and the thirddemand capacity; determining a spanning subset of the service linkscontaining the first and second service links; and configuring thecommunications network to satisfy the first, second, and third demandsusing the spanning subset of the service links.

44. A method for determining a spanning set of service links for acommunications network, comprising: obtaining a graph including a firstnumber of edges, the graph representing the communications network;obtaining transceiver data types including: a first transceiver datatype with a first weight, wherein a service link configured to use thefirst transceiver data type is capable of: spanning one edge of thegraph; and satisfying a set of demands on the communications network; asecond transceiver data type with a second weight, wherein a servicelink configured to use the second transceiver data type is capable of:spanning two edges of the graph; and satisfying at most some of thedemands in the set of demands; a third transceiver data type with athird weight, wherein a service link configured to use the thirdtransceiver data type is capable of: spanning three edges of the graph;and satisfying one of the demands in the set of demands; selecting,based on the first weight, second weight, third weight, and first numberof edges, service links that satisfy the demands, the selected servicelinks including: a first number of service links having the secondtransceiver data type, the first number of service links equal to thefirst number of edges; a service link having the first transceiver datatype and a second number of service links having the second transceiverdata type, the second number of service links equal to the first numberof edges minus one; four service links having the third transceiver datatype and a third number of service links having the second transceiverdata type, the third number of service links equal to the first numberof edges minus three; a fourth number of service links having the thirdtransceiver data type, the fourth number of service links equal to fourthirds times the first number of edges; a service link having the firsttransceiver data type and a fifth number of service links having thethird transceiver data type, the fifth number of service links equal tofour thirds times the first number of edges minus one; or two servicelinks having the second transceiver data type and a sixth number ofservice links having the third transceiver data type, the sixth numberof service links equal to four thirds times the first number of edgesminus two; and configuring the communications network to satisfy the setof demands using the selected service links.

44. A method for managing a communication network comprising at leastone of determining a spanning subset of service links as recited in anyone of clauses 1 to 10; configuring the communications network asrecited in any one of clauses 11 to 20; configuring the communicationsnetwork as recited in any one of clauses 21 to 31; or determining aconfiguration of the communications network as recited in any one ofclauses 32 to 42.

Other embodiments will be apparent from consideration of thespecification and practice of the embodiments disclosed herein. It isintended that the specification and examples be considered as exampleonly, with a true scope and spirit of the disclosed embodiments beingindicated by the following claims.

What is claimed is:
 1. A method for determining a spanning subset ofservice links for a communications network, comprising: obtaining a setof permissible service link decompositions for the communicationsnetwork and a set of basic service links for the communications network;and generating the spanning subset, the generation including: selectinga decomposition of a first service link from the set of permissibleservice link decompositions, the first service link being associatedwith a first demand; updating the set of permissible service linkdecompositions based on the selected decomposition, the updatingcomprising: removing, from the set of permissible service linkdecompositions, decompositions of the first service link or includingthe first service link; updating demands associated with service linksincluded in the selected decomposition using the first demand; andremoving decompositions that, based on the updated demands, violate acapacity constraint; and updating the set of basic service links usingthe updated set of permissible service link decompositions.
 2. Themethod of claim 1, wherein: selecting the decomposition of the firstservice link comprises: determining that the decomposition includes onlyservice links in the set of basic service links; and selecting thedecomposition in response to the determination.
 3. The method of claim1, wherein: updating the set of basic service links using the updatedset of permissible service link decompositions comprises: determiningthat the updated set of permissible service link decompositions lacks anon-trivial decomposition of a second service link; and adding thesecond service link to the set of basic service links in response to thedetermination.
 4. The method of claim 1, wherein: the set of basicservice links is updated to include ones of the service links that lacknon-trivial decompositions in the updated set of permissible servicelink decompositions.
 5. The method of claim 1, wherein: generation ofthe spanning subset further includes: updating the set of permissibleservice link decompositions based on the updated set of basic servicelinks.
 6. The method of claim 1, wherein: obtaining the set ofpermissible service link decompositions comprises: generating a set ofpermissible service link decompositions for each one of the servicelinks, the generation comprising: selecting a subset of the servicelinks based on a path of the each one of the service links and a seconddemand; generating a decomposition graph using the subset of the servicelinks; and generating the set of permissible service link decompositionsfor the each one of the services links using the decomposition graph. 7.The method of claim 1, wherein: obtaining the set of permissible servicelink decompositions comprises generating and traversing a decompositiongraph for each of the service links.
 8. The method of claim 1, wherein:the method further comprises configuring the communications network totransmit network traffic using the spanning subset of service links. 9.A method for configuring a communications network, comprising: obtaininga set of permissible decompositions of a set of service links for thecommunications network; iteratively determining a spanning subset of theset of service links, an iteration comprising: updating the spanningsubset of the set of service links based on the set of permissibleservice link decompositions; updating the set of permissible servicelink decompositions based on the spanning subset; selecting, from theset of permissible service link decompositions, a decomposition of afirst service link; and updating the set of permissible service linkdecompositions using a first demand associated with the first servicelink, the updating comprising: removing, from the set of permissibleservice link decompositions, decompositions of the first service link orincluding the first service link; updating, using the first demand,demands associated with service links included in the selecteddecomposition of the first service link; and removing decompositionsthat, based on the updated demands, violate a capacity constraint; andconfiguring the communications network to transmit network traffic usingthe spanning subset of the set of service links.
 10. The method of claim9, wherein: selecting the decomposition of the first service linkcomprises: determining that the decomposition consists of service linksin the spanning subset; and selecting the decomposition, at least inpart, in response to the determination.
 11. The method of claim 10,wherein: selecting the decomposition of the first service link furthercomprises: determining that no other decomposition consisting of servicelinks in the spanning subset includes more service links than theselected decomposition.
 12. The method of claim 9, wherein: updating thespanning subset using the updated set of permissible service linkdecompositions comprises: determining that the updated set ofpermissible service link decompositions lacks a non-trivialdecomposition of a second service link; and adding the second servicelink to the spanning subset in response to the determination.
 13. Themethod of claim 9, wherein: the spanning subset is updated to consist ofservice links lacking non-trivial decompositions in the updated set ofpermissible service link decompositions.
 14. The method of claim 9,wherein: obtaining the set of permissible service link decompositionscomprises: generating a set of permissible service link decompositionsfor the first service link, the generation comprising: selecting asubset of the service links based on a path of the first service linkand the first demand; generating a decomposition graph using theselected subset of the service links; and generating the set ofpermissible service link decompositions for the first service link usingthe decomposition graph.
 15. The method of claim 9, wherein: obtainingthe set of permissible service link decompositions comprises generatingand traversing a decomposition graph for each of the service links. 16.The method of claim 15, wherein: the decomposition graph is traversedusing a shortest path algorithm.